Finite Math Examples

$\frac{1}{28} \cdot ((21 + \sqrt{21}) (6 - 7 x)) = x$

Step 1

Simplify $\frac{1}{28} \cdot ((21 + \sqrt{21}) (6 - 7 x))$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{28} \cdot ((21 + \sqrt{21}) (6 - 7 x)) = x$

Step 1.2

Simplify by adding zeros.

$\frac{1}{28} \cdot ((21 + \sqrt{21}) (6 - 7 x)) = x$

Step 1.3

Expand $(21 + \sqrt{21}) (6 - 7 x)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$\frac{1}{28} \cdot (21 (6 - 7 x) + \sqrt{21} (6 - 7 x)) = x$

Step 1.3.2

Apply the distributive property.

$\frac{1}{28} \cdot (21 \cdot 6 + 21 (- 7 x) + \sqrt{21} (6 - 7 x)) = x$

Step 1.3.3

Apply the distributive property.

$\frac{1}{28} \cdot (21 \cdot 6 + 21 (- 7 x) + \sqrt{21} \cdot 6 + \sqrt{21} (- 7 x)) = x$

Step 1.4

Simplify terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $21$ by $6$ .

$\frac{1}{28} \cdot (126 + 21 (- 7 x) + \sqrt{21} \cdot 6 + \sqrt{21} (- 7 x)) = x$

Step 1.4.1.2

Multiply $- 7$ by $21$ .

$\frac{1}{28} \cdot (126 - 147 x + \sqrt{21} \cdot 6 + \sqrt{21} (- 7 x)) = x$

Step 1.4.1.3

Move $6$ to the left of $\sqrt{21}$ .

$\frac{1}{28} \cdot (126 - 147 x + 6 \sqrt{21} + \sqrt{21} (- 7 x)) = x$

Step 1.4.2

Apply the distributive property.

$\frac{1}{28} \cdot 126 + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5

Simplify.

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Step 1.5.1

Cancel the common factor of $14$ .

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Step 1.5.1.1

Factor $14$ out of $28$ .

$\frac{1}{14 (2)} \cdot 126 + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.1.2

Factor $14$ out of $126$ .

$\frac{1}{14 \cdot 2} \cdot (14 \cdot 9) + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.1.3

Cancel the common factor.

$\frac{1}{14 \cdot 2} \cdot (14 \cdot 9) + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.1.4

Rewrite the expression.

$\frac{1}{2} \cdot 9 + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.2

Combine $\frac{1}{2}$ and $9$ .

$\frac{9}{2} + \frac{1}{28} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.3

Cancel the common factor of $7$ .

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Step 1.5.3.1

Factor $7$ out of $28$ .

$\frac{9}{2} + \frac{1}{7 (4)} (- 147 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.3.2

Factor $7$ out of $- 147 x$ .

$\frac{9}{2} + \frac{1}{7 (4)} (7 (- 21 x)) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.3.3

Cancel the common factor.

$\frac{9}{2} + \frac{1}{7 \cdot 4} (7 (- 21 x)) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.3.4

Rewrite the expression.

$\frac{9}{2} + \frac{1}{4} (- 21 x) + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.4

Combine $- 21$ and $\frac{1}{4}$ .

$\frac{9}{2} + \frac{- 21}{4} x + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.5

Combine $\frac{- 21}{4}$ and $x$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{1}{28} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.6

Cancel the common factor of $2$ .

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Step 1.5.6.1

Factor $2$ out of $28$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{1}{2 (14)} (6 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.6.2

Factor $2$ out of $6 \sqrt{21}$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{1}{2 (14)} (2 (3 \sqrt{21})) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.6.3

Cancel the common factor.

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{1}{2 \cdot 14} (2 (3 \sqrt{21})) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.6.4

Rewrite the expression.

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{1}{14} (3 \sqrt{21}) + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.7

Combine $3$ and $\frac{1}{14}$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3}{14} \sqrt{21} + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.8

Combine $\frac{3}{14}$ and $\sqrt{21}$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{1}{28} (\sqrt{21} (- 7 x)) = x$

Step 1.5.9

Cancel the common factor of $7$ .

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Step 1.5.9.1

Factor $7$ out of $28$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{1}{7 (4)} (\sqrt{21} (- 7 x)) = x$

Step 1.5.9.2

Factor $7$ out of $\sqrt{21} (- 7 x)$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{1}{7 (4)} (7 (\sqrt{21} (- x))) = x$

Step 1.5.9.3

Cancel the common factor.

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{1}{7 \cdot 4} (7 (\sqrt{21} (- x))) = x$

Step 1.5.9.4

Rewrite the expression.

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{1}{4} (\sqrt{21} (- x)) = x$

Step 1.5.10

Combine $\sqrt{21}$ and $\frac{1}{4}$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} + \frac{\sqrt{21}}{4} (- x) = x$

Step 1.5.11

Combine $\frac{\sqrt{21}}{4}$ and $x$ .

$\frac{9}{2} + \frac{- 21 x}{4} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} = x$

Step 1.6

Move the negative in front of the fraction.

$\frac{9}{2} - \frac{21 x}{4} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} = x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{9}{2} - \frac{21 x}{4} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} - x = 0$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} - \frac{21 x}{4} - x \cdot \frac{4}{4} = 0$

Step 2.3

Combine $- x$ and $\frac{4}{4}$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} - \frac{21 x}{4} + \frac{- x \cdot 4}{4} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} - \frac{\sqrt{21} x}{4} + \frac{- 21 x - x \cdot 4}{4} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{- \sqrt{21} x - 21 x - x \cdot 4}{4} = 0$

Step 2.6

Multiply $4$ by $- 1$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{- \sqrt{21} x - 21 x - 4 x}{4} = 0$

Step 2.7

Subtract $4 x$ from $- 21 x$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{- \sqrt{21} x - 25 x}{4} = 0$

Step 2.8

Factor $x$ out of $- \sqrt{21} x - 25 x$ .

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Step 2.8.1

Factor $x$ out of $- \sqrt{21} x$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{x (- \sqrt{21}) - 25 x}{4} = 0$

Step 2.8.2

Factor $x$ out of $- 25 x$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{x (- \sqrt{21}) + x \cdot - 25}{4} = 0$

Step 2.8.3

Factor $x$ out of $x (- \sqrt{21}) + x \cdot - 25$ .

$\frac{9}{2} + \frac{3 \sqrt{21}}{14} + \frac{x (- \sqrt{21} - 25)}{4} = 0$

Step 2.9

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} \cdot \frac{2}{2} + \frac{x (- \sqrt{21} - 25)}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.10

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.10.1

Multiply $\frac{9}{2}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{2 \cdot 2} + \frac{x (- \sqrt{21} - 25)}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.10.2

Multiply $2$ by $2$ .

$\frac{9 \cdot 2}{4} + \frac{x (- \sqrt{21} - 25)}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.11

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 + x (- \sqrt{21} - 25)}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.12

Multiply $9$ by $2$ .

$\frac{18 + x (- \sqrt{21} - 25)}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.13

Simplify the numerator.

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Step 2.13.1

Apply the distributive property.

$\frac{18 + x (- \sqrt{21}) + x \cdot - 25}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.13.2

Move $- 25$ to the left of $x$ .

$\frac{18 + x (- \sqrt{21}) - 25 \cdot x}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.13.3

Reorder terms.

$\frac{- x \sqrt{21} - 25 x + 18}{4} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.14

To write $\frac{- x \sqrt{21} - 25 x + 18}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{- x \sqrt{21} - 25 x + 18}{4} \cdot \frac{7}{7} + \frac{3 \sqrt{21}}{14} = 0$

Step 2.15

To write $\frac{3 \sqrt{21}}{14}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- x \sqrt{21} - 25 x + 18}{4} \cdot \frac{7}{7} + \frac{3 \sqrt{21}}{14} \cdot \frac{2}{2} = 0$

Step 2.16

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.16.1

Multiply $\frac{- x \sqrt{21} - 25 x + 18}{4}$ by $\frac{7}{7}$ .

$\frac{(- x \sqrt{21} - 25 x + 18) \cdot 7}{4 \cdot 7} + \frac{3 \sqrt{21}}{14} \cdot \frac{2}{2} = 0$

Step 2.16.2

Multiply $4$ by $7$ .

$\frac{(- x \sqrt{21} - 25 x + 18) \cdot 7}{28} + \frac{3 \sqrt{21}}{14} \cdot \frac{2}{2} = 0$

Step 2.16.3

Multiply $\frac{3 \sqrt{21}}{14}$ by $\frac{2}{2}$ .

$\frac{(- x \sqrt{21} - 25 x + 18) \cdot 7}{28} + \frac{3 \sqrt{21} \cdot 2}{14 \cdot 2} = 0$

Step 2.16.4

Multiply $14$ by $2$ .

$\frac{(- x \sqrt{21} - 25 x + 18) \cdot 7}{28} + \frac{3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.17

Combine the numerators over the common denominator.

$\frac{(- x \sqrt{21} - 25 x + 18) \cdot 7 + 3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.18

Simplify the numerator.

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Step 2.18.1

Apply the distributive property.

$\frac{- x \sqrt{21} \cdot 7 - 25 x \cdot 7 + 18 \cdot 7 + 3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.18.2

Simplify.

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Step 2.18.2.1

Multiply $7$ by $- 1$ .

$\frac{- 7 x \sqrt{21} - 25 x \cdot 7 + 18 \cdot 7 + 3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.18.2.2

Multiply $7$ by $- 25$ .

$\frac{- 7 x \sqrt{21} - 175 x + 18 \cdot 7 + 3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.18.2.3

Multiply $18$ by $7$ .

$\frac{- 7 x \sqrt{21} - 175 x + 126 + 3 \sqrt{21} \cdot 2}{28} = 0$

Step 2.18.3

Multiply $2$ by $3$ .

$\frac{- 7 x \sqrt{21} - 175 x + 126 + 6 \sqrt{21}}{28} = 0$

Step 2.19

Factor $- 1$ out of $- 7 x \sqrt{21}$ .

$\frac{- (7 x \sqrt{21}) - 175 x + 126 + 6 \sqrt{21}}{28} = 0$

Step 2.20

Factor $- 1$ out of $- 175 x$ .

$\frac{- (7 x \sqrt{21}) - (175 x) + 126 + 6 \sqrt{21}}{28} = 0$

Step 2.21

Factor $- 1$ out of $- (7 x \sqrt{21}) - (175 x)$ .

$\frac{- (7 x \sqrt{21} + 175 x) + 126 + 6 \sqrt{21}}{28} = 0$

Step 2.22

Rewrite $126$ as $- 1 (- 126)$ .

$\frac{- (7 x \sqrt{21} + 175 x) - 1 (- 126) + 6 \sqrt{21}}{28} = 0$

Step 2.23

Factor $- 1$ out of $- (7 x \sqrt{21} + 175 x) - 1 (- 126)$ .

$\frac{- (7 x \sqrt{21} + 175 x - 126) + 6 \sqrt{21}}{28} = 0$

Step 2.24

Factor $- 1$ out of $6 \sqrt{21}$ .

$\frac{- (7 x \sqrt{21} + 175 x - 126) - (- 6 \sqrt{21})}{28} = 0$

Step 2.25

Factor $- 1$ out of $- (7 x \sqrt{21} + 175 x - 126) - (- 6 \sqrt{21})$ .

$\frac{- (7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21})}{28} = 0$

Step 2.26

Rewrite $- (7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21})$ as $- 1 (7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21})$ .

$\frac{- 1 (7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21})}{28} = 0$

Step 2.27

Move the negative in front of the fraction.

$- \frac{7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21}}{28} = 0$

Step 3

Set the numerator equal to zero.

$7 x \sqrt{21} + 175 x - 126 - 6 \sqrt{21} = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1.1

Add $126$ to both sides of the equation.

$7 x \sqrt{21} + 175 x - 6 \sqrt{21} = 126$

Step 4.1.2

Add $6 \sqrt{21}$ to both sides of the equation.

$7 x \sqrt{21} + 175 x = 126 + 6 \sqrt{21}$

Step 4.2

Factor $7 x$ out of $7 x \sqrt{21} + 175 x$ .

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Step 4.2.1

Factor $7 x$ out of $7 x \sqrt{21}$ .

$7 x (\sqrt{21}) + 175 x = 126 + 6 \sqrt{21}$

Step 4.2.2

Factor $7 x$ out of $175 x$ .

$7 x (\sqrt{21}) + 7 x (25) = 126 + 6 \sqrt{21}$

Step 4.2.3

Factor $7 x$ out of $7 x (\sqrt{21}) + 7 x (25)$ .

$7 x (\sqrt{21} + 25) = 126 + 6 \sqrt{21}$

Step 4.3

Divide each term in $7 x (\sqrt{21} + 25) = 126 + 6 \sqrt{21}$ by $7 \sqrt{21} + 175$ and simplify.

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Step 4.3.1

Divide each term in $7 x (\sqrt{21} + 25) = 126 + 6 \sqrt{21}$ by $7 \sqrt{21} + 175$ .

$\frac{7 x (\sqrt{21} + 25)}{7 \sqrt{21} + 175} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $7$ and $7 \sqrt{21} + 175$ .

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Step 4.3.2.1.1

Factor $7$ out of $7 x (\sqrt{21} + 25)$ .

$\frac{7 (x (\sqrt{21} + 25))}{7 \sqrt{21} + 175} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.1.2

Cancel the common factors.

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Step 4.3.2.1.2.1

Factor $7$ out of $7 \sqrt{21}$ .

$\frac{7 (x (\sqrt{21} + 25))}{7 (\sqrt{21}) + 175} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.1.2.2

Factor $7$ out of $175$ .

$\frac{7 (x (\sqrt{21} + 25))}{7 \sqrt{21} + 7 \cdot 25} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.1.2.3

Factor $7$ out of $7 \sqrt{21} + 7 \cdot 25$ .

$\frac{7 (x (\sqrt{21} + 25))}{7 (\sqrt{21} + 25)} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.1.2.4

Cancel the common factor.

$\frac{7 (x (\sqrt{21} + 25))}{7 (\sqrt{21} + 25)} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.1.2.5

Rewrite the expression.

$\frac{x (\sqrt{21} + 25)}{\sqrt{21} + 25} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.2

Cancel the common factor of $\sqrt{21} + 25$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{x (\sqrt{21} + 25)}{\sqrt{21} + 25} = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{126}{7 \sqrt{21} + 175} + \frac{6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Combine the numerators over the common denominator.

$x = \frac{126 + 6 \sqrt{21}}{7 \sqrt{21} + 175}$

Step 4.3.3.2

Multiply $\frac{126 + 6 \sqrt{21}}{7 \sqrt{21} + 175}$ by $\frac{7 \sqrt{21} - 175}{7 \sqrt{21} - 175}$ .

$x = \frac{126 + 6 \sqrt{21}}{7 \sqrt{21} + 175} \cdot \frac{7 \sqrt{21} - 175}{7 \sqrt{21} - 175}$

Step 4.3.3.3

Simplify terms.

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Step 4.3.3.3.1

Multiply $\frac{126 + 6 \sqrt{21}}{7 \sqrt{21} + 175}$ by $\frac{7 \sqrt{21} - 175}{7 \sqrt{21} - 175}$ .

$x = \frac{(126 + 6 \sqrt{21}) (7 \sqrt{21} - 175)}{(7 \sqrt{21} + 175) (7 \sqrt{21} - 175)}$

Step 4.3.3.3.2

Expand the denominator using the FOIL method.

$x = \frac{(126 + 6 \sqrt{21}) (7 \sqrt{21} - 175)}{49 {\sqrt{21}}^{2} - 1225 \sqrt{21} + 1225 \sqrt{21} - 30625}$

Step 4.3.3.3.3

Simplify.

$x = \frac{(126 + 6 \sqrt{21}) (7 \sqrt{21} - 175)}{- 29596}$

Step 4.3.3.3.4

Cancel the common factor of $126 + 6 \sqrt{21}$ and $- 29596$ .

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Step 4.3.3.3.4.1

Factor $2$ out of $(126 + 6 \sqrt{21}) (7 \sqrt{21} - 175)$ .

$x = \frac{2 ((63 + 3 \sqrt{21}) (7 \sqrt{21} - 175))}{- 29596}$

Step 4.3.3.3.4.2

Cancel the common factors.

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Step 4.3.3.3.4.2.1

Factor $2$ out of $- 29596$ .

$x = \frac{2 ((63 + 3 \sqrt{21}) (7 \sqrt{21} - 175))}{2 (- 14798)}$

Step 4.3.3.3.4.2.2

Cancel the common factor.

$x = \frac{2 ((63 + 3 \sqrt{21}) (7 \sqrt{21} - 175))}{2 \cdot - 14798}$

Step 4.3.3.3.4.2.3

Rewrite the expression.

$x = \frac{(63 + 3 \sqrt{21}) (7 \sqrt{21} - 175)}{- 14798}$

Step 4.3.3.3.5

Cancel the common factor of $7 \sqrt{21} - 175$ and $- 14798$ .

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Step 4.3.3.3.5.1

Factor $7$ out of $(63 + 3 \sqrt{21}) (7 \sqrt{21} - 175)$ .

$x = \frac{7 ((63 + 3 \sqrt{21}) (\sqrt{21} - 25))}{- 14798}$

Step 4.3.3.3.5.2

Cancel the common factors.

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Step 4.3.3.3.5.2.1

Factor $7$ out of $- 14798$ .

$x = \frac{7 ((63 + 3 \sqrt{21}) (\sqrt{21} - 25))}{7 (- 2114)}$

Step 4.3.3.3.5.2.2

Cancel the common factor.

$x = \frac{7 ((63 + 3 \sqrt{21}) (\sqrt{21} - 25))}{7 \cdot - 2114}$

Step 4.3.3.3.5.2.3

Rewrite the expression.

$x = \frac{(63 + 3 \sqrt{21}) (\sqrt{21} - 25)}{- 2114}$

Step 4.3.3.4

Expand $(63 + 3 \sqrt{21}) (\sqrt{21} - 25)$ using the FOIL Method.

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Step 4.3.3.4.1

Apply the distributive property.

$x = \frac{63 (\sqrt{21} - 25) + 3 \sqrt{21} (\sqrt{21} - 25)}{- 2114}$

Step 4.3.3.4.2

Apply the distributive property.

$x = \frac{63 \sqrt{21} + 63 \cdot - 25 + 3 \sqrt{21} (\sqrt{21} - 25)}{- 2114}$

Step 4.3.3.4.3

Apply the distributive property.

$x = \frac{63 \sqrt{21} + 63 \cdot - 25 + 3 \sqrt{21} \sqrt{21} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5

Simplify and combine like terms.

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Step 4.3.3.5.1

Simplify each term.

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Step 4.3.3.5.1.1

Multiply $63$ by $- 25$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 \sqrt{21} \sqrt{21} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.2

Multiply $3 \sqrt{21} \sqrt{21}$ .

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Step 4.3.3.5.1.2.1

Raise $\sqrt{21}$ to the power of $1$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 ({\sqrt{21}}^{1} \sqrt{21}) + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.2.2

Raise $\sqrt{21}$ to the power of $1$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 ({\sqrt{21}}^{1} {\sqrt{21}}^{1}) + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{63 \sqrt{21} - 1575 + 3 {\sqrt{21}}^{1 + 1} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.2.4

Add $1$ and $1$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 {\sqrt{21}}^{2} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3

Rewrite ${\sqrt{21}}^{2}$ as $21$ .

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Step 4.3.3.5.1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{21}$ as $21^{\frac{1}{2}}$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 {(21^{\frac{1}{2}})}^{2} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 \cdot 21^{\frac{1}{2} \cdot 2} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3.3

Combine $\frac{1}{2}$ and $2$ .

$x = \frac{63 \sqrt{21} - 1575 + 3 \cdot 21^{\frac{2}{2}} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3.4

Cancel the common factor of $2$ .

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Step 4.3.3.5.1.3.4.1

Cancel the common factor.

$x = \frac{63 \sqrt{21} - 1575 + 3 \cdot 21^{\frac{2}{2}} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3.4.2

Rewrite the expression.

$x = \frac{63 \sqrt{21} - 1575 + 3 \cdot 21^{1} + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.3.5

Evaluate the exponent.

$x = \frac{63 \sqrt{21} - 1575 + 3 \cdot 21 + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.4

Multiply $3$ by $21$ .

$x = \frac{63 \sqrt{21} - 1575 + 63 + 3 \sqrt{21} \cdot - 25}{- 2114}$

Step 4.3.3.5.1.5

Multiply $- 25$ by $3$ .

$x = \frac{63 \sqrt{21} - 1575 + 63 - 75 \sqrt{21}}{- 2114}$

Step 4.3.3.5.2

Subtract $75 \sqrt{21}$ from $63 \sqrt{21}$ .

$x = \frac{- 1575 + 63 - 12 \sqrt{21}}{- 2114}$

Step 4.3.3.5.3

Add $- 1575$ and $63$ .

$x = \frac{- 1512 - 12 \sqrt{21}}{- 2114}$

Step 4.3.3.6

Cancel the common factor of $- 1512 - 12 \sqrt{21}$ and $- 2114$ .

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Step 4.3.3.6.1

Factor $2$ out of $- 1512$ .

$x = \frac{2 (- 756) - 12 \sqrt{21}}{- 2114}$

Step 4.3.3.6.2

Factor $2$ out of $- 12 \sqrt{21}$ .

$x = \frac{2 (- 756) + 2 (- 6 \sqrt{21})}{- 2114}$

Step 4.3.3.6.3

Factor $2$ out of $2 (- 756) + 2 (- 6 \sqrt{21})$ .

$x = \frac{2 (- 756 - 6 \sqrt{21})}{- 2114}$

Step 4.3.3.6.4

Cancel the common factors.

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Step 4.3.3.6.4.1

Factor $2$ out of $- 2114$ .

$x = \frac{2 (- 756 - 6 \sqrt{21})}{2 \cdot - 1057}$

Step 4.3.3.6.4.2

Cancel the common factor.

$x = \frac{2 (- 756 - 6 \sqrt{21})}{2 \cdot - 1057}$

Step 4.3.3.6.4.3

Rewrite the expression.

$x = \frac{- 756 - 6 \sqrt{21}}{- 1057}$

Step 4.3.3.7

Move the negative in front of the fraction.

$x = - \frac{- 756 - 6 \sqrt{21}}{1057}$

Step 4.3.3.8

Rewrite $- 756$ as $- 1 (756)$ .

$x = - \frac{- 1 (756) - 6 \sqrt{21}}{1057}$

Step 4.3.3.9

Factor $- 1$ out of $- 6 \sqrt{21}$ .

$x = - \frac{- 1 (756) - (6 \sqrt{21})}{1057}$

Step 4.3.3.10

Factor $- 1$ out of $- 1 (756) - (6 \sqrt{21})$ .

$x = - \frac{- 1 (756 + 6 \sqrt{21})}{1057}$

Step 4.3.3.11

Simplify the expression.

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Step 4.3.3.11.1

Move the negative in front of the fraction.

$x = - - \frac{756 + 6 \sqrt{21}}{1057}$

Step 4.3.3.11.2

Multiply $- 1$ by $- 1$ .

$x = 1 \frac{756 + 6 \sqrt{21}}{1057}$

Step 4.3.3.11.3

Multiply $\frac{756 + 6 \sqrt{21}}{1057}$ by $1$ .

$x = \frac{756 + 6 \sqrt{21}}{1057}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{756 + 6 \sqrt{21}}{1057}$

Decimal Form:

$x = 0.74124451 \dots$