Basic Math Examples

4 {(9 - x)}^{0.5} - 6 = 10

$4 {(9 - x)}^{0.5} - 6 = 10$

Step 1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 1.1

Add

6

$6$ to both sides of the equation.

4 {(9 - x)}^{0.5} = 10 + 6

$4 {(9 - x)}^{0.5} = 10 + 6$

Step 1.2

Add

10

$10$ and

6

$6$ .

4 {(9 - x)}^{0.5} = 16

$4 {(9 - x)}^{0.5} = 16$

4 {(9 - x)}^{0.5} = 16

$4 {(9 - x)}^{0.5} = 16$

Step 2

Divide each term in

4 {(9 - x)}^{0.5} = 16

$4 {(9 - x)}^{0.5} = 16$ by

4

$4$ and simplify.

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Step 2.1

Divide each term in

4 {(9 - x)}^{0.5} = 16

$4 {(9 - x)}^{0.5} = 16$ by

4

$4$ .

\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}

$\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

4

$4$ .

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Step 2.2.1.1

Cancel the common factor.

\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}

$\frac{4 {(9 - x)}^{0.5}}{4} = \frac{16}{4}$

Step 2.2.1.2

Divide

{(9 - x)}^{0.5}

${(9 - x)}^{0.5}$ by

1

$1$ .

{(9 - x)}^{0.5} = \frac{16}{4}

${(9 - x)}^{0.5} = \frac{16}{4}$

{(9 - x)}^{0.5} = \frac{16}{4}

${(9 - x)}^{0.5} = \frac{16}{4}$

{(9 - x)}^{0.5} = \frac{16}{4}

${(9 - x)}^{0.5} = \frac{16}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide

16

$16$ by

4

$4$ .

{(9 - x)}^{0.5} = 4

${(9 - x)}^{0.5} = 4$

{(9 - x)}^{0.5} = 4

${(9 - x)}^{0.5} = 4$

{(9 - x)}^{0.5} = 4

${(9 - x)}^{0.5} = 4$

Step 3

Convert the decimal exponent to a fractional exponent.

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Step 3.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is

1

$1$ number to the right of the decimal point, place the decimal number over

10^{1}

$10^{1}$

(10)

$(10)$ . Next, add the whole number to the left of the decimal.

{(9 - x)}^{0 \frac{5}{10}} = 4

${(9 - x)}^{0 \frac{5}{10}} = 4$

Step 3.2

Reduce the fraction.

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Step 3.2.1

Convert

0 \frac{5}{10}

$0 \frac{5}{10}$ to an improper fraction.

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Step 3.2.1.1

A mixed number is an addition of its whole and fractional parts.

{(9 - x)}^{0 + \frac{5}{10}} = 4

${(9 - x)}^{0 + \frac{5}{10}} = 4$

Step 3.2.1.2

Add

0

$0$ and

\frac{5}{10}

$\frac{5}{10}$ .

{(9 - x)}^{\frac{5}{10}} = 4

${(9 - x)}^{\frac{5}{10}} = 4$

{(9 - x)}^{\frac{5}{10}} = 4

${(9 - x)}^{\frac{5}{10}} = 4$

Step 3.2.2

Cancel the common factor of

5

$5$ and

10

$10$ .

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Step 3.2.2.1

Factor

5

$5$ out of

5

$5$ .

{(9 - x)}^{\frac{5 (1)}{10}} = 4

${(9 - x)}^{\frac{5 (1)}{10}} = 4$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor

5

$5$ out of

10

$10$ .

{(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4

${(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4$

Step 3.2.2.2.2

Cancel the common factor.

{(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4

${(9 - x)}^{\frac{5 \cdot 1}{5 \cdot 2}} = 4$

Step 3.2.2.2.3

Rewrite the expression.

{(9 - x)}^{\frac{1}{2}} = 4

${(9 - x)}^{\frac{1}{2}} = 4$

{(9 - x)}^{\frac{1}{2}} = 4

${(9 - x)}^{\frac{1}{2}} = 4$

{(9 - x)}^{\frac{1}{2}} = 4

${(9 - x)}^{\frac{1}{2}} = 4$

{(9 - x)}^{\frac{1}{2}} = 4

${(9 - x)}^{\frac{1}{2}} = 4$

{(9 - x)}^{\frac{1}{2}} = 4

${(9 - x)}^{\frac{1}{2}} = 4$

Step 4

Raise each side of the equation to the power of

\frac{1}{0.5}

$\frac{1}{0.5}$ to eliminate the fractional exponent on the left side.

{({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}} = 4^{\frac{1}{0.5}}

${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5

Simplify the exponent.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

{({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}

${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

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Step 5.1.1.1

Multiply the exponents in

{({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}

${({(9 - x)}^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

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Step 5.1.1.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

{(9 - x)}^{\frac{1}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}

${(9 - x)}^{\frac{1}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2

Cancel the common factor of

0.5

$0.5$ .

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Step 5.1.1.1.2.1

Factor

0.5

$0.5$ out of

1

$1$ .

{(9 - x)}^{\frac{0.5 (2)}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}

${(9 - x)}^{\frac{0.5 (2)}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2.2

Cancel the common factor.

{(9 - x)}^{\frac{0.5 \cdot 2}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}

${(9 - x)}^{\frac{0.5 \cdot 2}{2} \cdot \frac{1}{0.5}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.2.3

Rewrite the expression.

{(9 - x)}^{\frac{2}{2}} = 4^{\frac{1}{0.5}}

${(9 - x)}^{\frac{2}{2}} = 4^{\frac{1}{0.5}}$

{(9 - x)}^{\frac{2}{2}} = 4^{\frac{1}{0.5}}

${(9 - x)}^{\frac{2}{2}} = 4^{\frac{1}{0.5}}$

Step 5.1.1.1.3

Divide

2

$2$ by

2

$2$ .

{(9 - x)}^{1} = 4^{\frac{1}{0.5}}

${(9 - x)}^{1} = 4^{\frac{1}{0.5}}$

{(9 - x)}^{1} = 4^{\frac{1}{0.5}}

${(9 - x)}^{1} = 4^{\frac{1}{0.5}}$

Step 5.1.1.2

Simplify.

9 - x = 4^{\frac{1}{0.5}}

$9 - x = 4^{\frac{1}{0.5}}$

9 - x = 4^{\frac{1}{0.5}}

$9 - x = 4^{\frac{1}{0.5}}$

9 - x = 4^{\frac{1}{0.5}}

$9 - x = 4^{\frac{1}{0.5}}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

4^{\frac{1}{0.5}}

$4^{\frac{1}{0.5}}$ .

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Step 5.2.1.1

Divide

1

$1$ by

0.5

$0.5$ .

9 - x = 4^{2}

$9 - x = 4^{2}$

Step 5.2.1.2

Raise

4

$4$ to the power of

2

$2$ .

9 - x = 16

$9 - x = 16$

9 - x = 16

$9 - x = 16$

9 - x = 16

$9 - x = 16$

9 - x = 16

$9 - x = 16$

Step 6

Solve for

x

$x$ .

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Step 6.1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 6.1.1

Subtract

9

$9$ from both sides of the equation.

- x = 16 - 9

$- x = 16 - 9$

Step 6.1.2

Subtract

9

$9$ from

16

$16$ .

- x = 7

$- x = 7$

- x = 7

$- x = 7$

Step 6.2

Divide each term in

- x = 7

$- x = 7$ by

- 1

$- 1$ and simplify.

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Step 6.2.1

Divide each term in

- x = 7

$- x = 7$ by

- 1

$- 1$ .

\frac{- x}{- 1} = \frac{7}{- 1}

$\frac{- x}{- 1} = \frac{7}{- 1}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Dividing two negative values results in a positive value.

\frac{x}{1} = \frac{7}{- 1}

$\frac{x}{1} = \frac{7}{- 1}$

Step 6.2.2.2

Divide

x

$x$ by

1

$1$ .

x = \frac{7}{- 1}

$x = \frac{7}{- 1}$

x = \frac{7}{- 1}

$x = \frac{7}{- 1}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide

7

$7$ by

- 1

$- 1$ .

x = - 7

$x = - 7$

x = - 7

$x = - 7$

x = - 7

$x = - 7$

x = - 7

$x = - 7$