Finite Math Examples

${(x - 0.5)}^{2} + {(y + 0.5)}^{2} = {(4)}^{2}$

Step 1

Subtract ${(4)}^{2}$ from both sides of the equation.

${(x - 0.5)}^{2} + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2

Simplify ${(x - 0.5)}^{2} + {(y + 0.5)}^{2} - {(4)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 0.5)}^{2}$ as $(x - 0.5) (x - 0.5)$ .

$(x - 0.5) (x - 0.5) + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.2

Expand $(x - 0.5) (x - 0.5)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$x (x - 0.5) - 0.5 (x - 0.5) + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 0.5 - 0.5 (x - 0.5) + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 0.5 - 0.5 x - 0.5 \cdot - 0.5 + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 0.5 - 0.5 x - 0.5 \cdot - 0.5 + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.3.1.2

Move $- 0.5$ to the left of $x$ .

$x^{2} - 0.5 \cdot x - 0.5 x - 0.5 \cdot - 0.5 + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.3.1.3

Multiply $- 0.5$ by $- 0.5$ .

$x^{2} - 0.5 x - 0.5 x + 0.25 + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.3.2

Subtract $0.5 x$ from $- 0.5 x$ .

$x^{2} - 1 x + 0.25 + {(y + 0.5)}^{2} - {(4)}^{2} = 0$

Step 2.1.4

Rewrite ${(y + 0.5)}^{2}$ as $(y + 0.5) (y + 0.5)$ .

$x^{2} - 1 x + 0.25 + (y + 0.5) (y + 0.5) - {(4)}^{2} = 0$

Step 2.1.5

Expand $(y + 0.5) (y + 0.5)$ using the FOIL Method.

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Step 2.1.5.1

Apply the distributive property.

$x^{2} - 1 x + 0.25 + y (y + 0.5) + 0.5 (y + 0.5) - {(4)}^{2} = 0$

Step 2.1.5.2

Apply the distributive property.

$x^{2} - 1 x + 0.25 + y \cdot y + y \cdot 0.5 + 0.5 (y + 0.5) - {(4)}^{2} = 0$

Step 2.1.5.3

Apply the distributive property.

$x^{2} - 1 x + 0.25 + y \cdot y + y \cdot 0.5 + 0.5 y + 0.5 \cdot 0.5 - {(4)}^{2} = 0$

Step 2.1.6

Simplify and combine like terms.

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Step 2.1.6.1

Simplify each term.

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Step 2.1.6.1.1

Multiply $y$ by $y$ .

$x^{2} - 1 x + 0.25 + y^{2} + y \cdot 0.5 + 0.5 y + 0.5 \cdot 0.5 - {(4)}^{2} = 0$

Step 2.1.6.1.2

Move $0.5$ to the left of $y$ .

$x^{2} - 1 x + 0.25 + y^{2} + 0.5 \cdot y + 0.5 y + 0.5 \cdot 0.5 - {(4)}^{2} = 0$

Step 2.1.6.1.3

Multiply $0.5$ by $0.5$ .

$x^{2} - 1 x + 0.25 + y^{2} + 0.5 y + 0.5 y + 0.25 - {(4)}^{2} = 0$

Step 2.1.6.2

Add $0.5 y$ and $0.5 y$ .

$x^{2} - 1 x + 0.25 + y^{2} + y + 0.25 - {(4)}^{2} = 0$

Step 2.1.7

Raise $4$ to the power of $2$ .

$x^{2} - 1 x + 0.25 + y^{2} + y + 0.25 - 1 \cdot 16 = 0$

Step 2.1.8

Multiply $- 1$ by $16$ .

$x^{2} - 1 x + 0.25 + y^{2} + y + 0.25 - 16 = 0$

Step 2.2

Add $0.25$ and $0.25$ .

$x^{2} - 1 x + y^{2} + y + 0.5 - 16 = 0$

Step 2.3

Subtract $16$ from $0.5$ .

$x^{2} - 1 x + y^{2} + y - 15.5 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 1$ , $b = - 1$ , and $c = y^{2} + y - 15.5$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot (y^{2} + y - 15.5))}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 5.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y - 4 \cdot - 15.5}}{2 \cdot 1}$

Step 5.1.4

Multiply $- 4$ by $- 15.5$ .

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y + 62}}{2 \cdot 1}$

Step 5.1.5

Add $1$ and $62$ .

$x = \frac{1 \pm \sqrt{- 4 y^{2} - 4 y + 63}}{2 \cdot 1}$

Step 5.1.6

Rewrite $- 4 y^{2} - 4 y + 63$ in a factored form.

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Step 5.1.6.1

Factor $1$ out of $- 4 y^{2} - 4 y + 63$ .

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Step 5.1.6.1.1

Factor $1$ out of $- 4 y^{2}$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) - 4 y + 63}}{2 \cdot 1}$

Step 5.1.6.1.2

Factor $1$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 63}}{2 \cdot 1}$

Step 5.1.6.1.3

Rewrite $63$ as $1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 1 (63)}}{2 \cdot 1}$

Step 5.1.6.1.4

Factor $1$ out of $1 (- 4 y^{2}) + 1 (- 4 y)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y) + 1 (63)}}{2 \cdot 1}$

Step 5.1.6.1.5

Factor $1$ out of $1 (- 4 y^{2} - 4 y) + 1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 5.1.6.2

Factor by grouping.

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Step 5.1.6.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 4 \cdot 63 = - 252$ and whose sum is $b = - 4$ .

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Step 5.1.6.2.1.1

Factor $- 4$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 5.1.6.2.1.2

Rewrite $- 4$ as $14$ plus $- 18$

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + (14 - 18) y + 63)}}{2 \cdot 1}$

Step 5.1.6.2.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + 14 y - 18 y + 63)}}{2 \cdot 1}$

Step 5.1.6.2.2

Factor out the greatest common factor from each group.

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Step 5.1.6.2.2.1

Group the first two terms and the last two terms.

$x = \frac{1 \pm \sqrt{1 ((- 4 y^{2} + 14 y) - 18 y + 63)}}{2 \cdot 1}$

Step 5.1.6.2.2.2

Factor out the greatest common factor (GCF) from each group.

$x = \frac{1 \pm \sqrt{1 (2 y (- 2 y + 7) + 9 (- 2 y + 7))}}{2 \cdot 1}$

Step 5.1.6.2.3

Factor the polynomial by factoring out the greatest common factor, $- 2 y + 7$ .

$x = \frac{1 \pm \sqrt{1 ((- 2 y + 7) (2 y + 9))}}{2 \cdot 1}$

$x = \frac{1 \pm \sqrt{1 (- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 5.1.6.3

Multiply $- 2 y + 7$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2}$

Step 6

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 6.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y - 4 \cdot - 15.5}}{2 \cdot 1}$

Step 6.1.4

Multiply $- 4$ by $- 15.5$ .

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y + 62}}{2 \cdot 1}$

Step 6.1.5

Add $1$ and $62$ .

$x = \frac{1 \pm \sqrt{- 4 y^{2} - 4 y + 63}}{2 \cdot 1}$

Step 6.1.6

Rewrite $- 4 y^{2} - 4 y + 63$ in a factored form.

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Step 6.1.6.1

Factor $1$ out of $- 4 y^{2} - 4 y + 63$ .

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Step 6.1.6.1.1

Factor $1$ out of $- 4 y^{2}$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) - 4 y + 63}}{2 \cdot 1}$

Step 6.1.6.1.2

Factor $1$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 63}}{2 \cdot 1}$

Step 6.1.6.1.3

Rewrite $63$ as $1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 1 (63)}}{2 \cdot 1}$

Step 6.1.6.1.4

Factor $1$ out of $1 (- 4 y^{2}) + 1 (- 4 y)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y) + 1 (63)}}{2 \cdot 1}$

Step 6.1.6.1.5

Factor $1$ out of $1 (- 4 y^{2} - 4 y) + 1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 6.1.6.2

Factor by grouping.

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Step 6.1.6.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 4 \cdot 63 = - 252$ and whose sum is $b = - 4$ .

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Step 6.1.6.2.1.1

Factor $- 4$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 6.1.6.2.1.2

Rewrite $- 4$ as $14$ plus $- 18$

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + (14 - 18) y + 63)}}{2 \cdot 1}$

Step 6.1.6.2.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + 14 y - 18 y + 63)}}{2 \cdot 1}$

Step 6.1.6.2.2

Factor out the greatest common factor from each group.

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Step 6.1.6.2.2.1

Group the first two terms and the last two terms.

$x = \frac{1 \pm \sqrt{1 ((- 4 y^{2} + 14 y) - 18 y + 63)}}{2 \cdot 1}$

Step 6.1.6.2.2.2

Factor out the greatest common factor (GCF) from each group.

$x = \frac{1 \pm \sqrt{1 (2 y (- 2 y + 7) + 9 (- 2 y + 7))}}{2 \cdot 1}$

Step 6.1.6.2.3

Factor the polynomial by factoring out the greatest common factor, $- 2 y + 7$ .

$x = \frac{1 \pm \sqrt{1 ((- 2 y + 7) (2 y + 9))}}{2 \cdot 1}$

$x = \frac{1 \pm \sqrt{1 (- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 6.1.6.3

Multiply $- 2 y + 7$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2}$

Step 6.3

Change the $\pm$ to $+$ .

$x = \frac{1 + \sqrt{(- 2 y + 7) (2 y + 9)}}{2}$

Step 6.4

Reorder the terms.

$x = \frac{\sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

Step 6.5

Cancel the common factor of $\sqrt{(- 2 y + 7) (2 y + 9)} + 1$ and $2$ .

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Step 6.5.1

Factor $- 1$ out of $\sqrt{(- 2 y + 7) (2 y + 9)}$ .

$x = \frac{- 1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) + 1}{2}$

Step 6.5.2

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

$x = \frac{- 1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) - 1 \cdot - 1}{2}$

Step 6.5.3

Factor $- 1$ out of $- 1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) - 1 (- 1)$ .

$x = \frac{- 1 (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1)}{2}$

Step 6.5.4

Factor $1$ out of $- 1 (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1)$ .

$x = \frac{1 (- (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1))}{2}$

Step 6.5.5

Cancel the common factors.

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Step 6.5.5.1

Rewrite $2$ as $1 (2)$ .

$x = \frac{1 (- (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1))}{1 (2)}$

Step 6.5.5.2

Cancel the common factor.

$x = \frac{1 (- (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1))}{1 \cdot 2}$

Step 6.5.5.3

Rewrite the expression.

$x = \frac{- (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1)}{2}$

Step 6.6

Simplify the numerator.

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Step 6.6.1

Factor $- 1$ out of $- \sqrt{(- 2 y + 7) (2 y + 9)} - 1$ .

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Step 6.6.1.1

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

$x = \frac{- (- \sqrt{(- 2 y + 7) (2 y + 9)} - 1 \cdot 1)}{2}$

Step 6.6.1.2

Factor $- 1$ out of $- \sqrt{(- 2 y + 7) (2 y + 9)} - 1 (1)$ .

$x = \frac{\sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

$x = \frac{1 (\sqrt{(- 2 y + 7) (2 y + 9)} + 1)}{2}$

Step 6.6.2

Combine exponents.

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Step 6.6.2.1

Factor out negative.

$x = \frac{\sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

Step 6.6.2.2

Multiply $- 1$ by $- 1$ .

$x = \frac{1 (\sqrt{(- 2 y + 7) (2 y + 9)} + 1)}{2}$

Step 6.6.2.3

Multiply $\sqrt{(- 2 y + 7) (2 y + 9)} + 1$ by $1$ .

$x = \frac{\sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

Step 7

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot (y^{2} + y - 15.5)}}{2 \cdot 1}$

Step 7.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y - 4 \cdot - 15.5}}{2 \cdot 1}$

Step 7.1.4

Multiply $- 4$ by $- 15.5$ .

$x = \frac{1 \pm \sqrt{1 - 4 y^{2} - 4 y + 62}}{2 \cdot 1}$

Step 7.1.5

Add $1$ and $62$ .

$x = \frac{1 \pm \sqrt{- 4 y^{2} - 4 y + 63}}{2 \cdot 1}$

Step 7.1.6

Rewrite $- 4 y^{2} - 4 y + 63$ in a factored form.

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Step 7.1.6.1

Factor $1$ out of $- 4 y^{2} - 4 y + 63$ .

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Step 7.1.6.1.1

Factor $1$ out of $- 4 y^{2}$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) - 4 y + 63}}{2 \cdot 1}$

Step 7.1.6.1.2

Factor $1$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 63}}{2 \cdot 1}$

Step 7.1.6.1.3

Rewrite $63$ as $1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2}) + 1 (- 4 y) + 1 (63)}}{2 \cdot 1}$

Step 7.1.6.1.4

Factor $1$ out of $1 (- 4 y^{2}) + 1 (- 4 y)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y) + 1 (63)}}{2 \cdot 1}$

Step 7.1.6.1.5

Factor $1$ out of $1 (- 4 y^{2} - 4 y) + 1 (63)$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 7.1.6.2

Factor by grouping.

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Step 7.1.6.2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 4 \cdot 63 = - 252$ and whose sum is $b = - 4$ .

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Step 7.1.6.2.1.1

Factor $- 4$ out of $- 4 y$ .

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} - 4 y + 63)}}{2 \cdot 1}$

Step 7.1.6.2.1.2

Rewrite $- 4$ as $14$ plus $- 18$

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + (14 - 18) y + 63)}}{2 \cdot 1}$

Step 7.1.6.2.1.3

Apply the distributive property.

$x = \frac{1 \pm \sqrt{1 (- 4 y^{2} + 14 y - 18 y + 63)}}{2 \cdot 1}$

Step 7.1.6.2.2

Factor out the greatest common factor from each group.

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Step 7.1.6.2.2.1

Group the first two terms and the last two terms.

$x = \frac{1 \pm \sqrt{1 ((- 4 y^{2} + 14 y) - 18 y + 63)}}{2 \cdot 1}$

Step 7.1.6.2.2.2

Factor out the greatest common factor (GCF) from each group.

$x = \frac{1 \pm \sqrt{1 (2 y (- 2 y + 7) + 9 (- 2 y + 7))}}{2 \cdot 1}$

Step 7.1.6.2.3

Factor the polynomial by factoring out the greatest common factor, $- 2 y + 7$ .

$x = \frac{1 \pm \sqrt{1 ((- 2 y + 7) (2 y + 9))}}{2 \cdot 1}$

$x = \frac{1 \pm \sqrt{1 (- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 7.1.6.3

Multiply $- 2 y + 7$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{(- 2 y + 7) (2 y + 9)}}{2}$

Step 7.3

Change the $\pm$ to $-$ .

$x = \frac{1 - \sqrt{(- 2 y + 7) (2 y + 9)}}{2}$

Step 7.4

Reorder the terms.

$x = \frac{- \sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

Step 7.5

Cancel the common factor of $- \sqrt{(- 2 y + 7) (2 y + 9)} + 1$ and $2$ .

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Step 7.5.1

Factor $1$ out of $- \sqrt{(- 2 y + 7) (2 y + 9)}$ .

$x = \frac{1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) + 1}{2}$

Step 7.5.2

Rewrite $1$ as $1 (1)$ .

$x = \frac{1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) + 1 (1)}{2}$

Step 7.5.3

Factor $1$ out of $1 (- \sqrt{(- 2 y + 7) (2 y + 9)}) + 1 (1)$ .

$x = \frac{1 (- \sqrt{(- 2 y + 7) (2 y + 9)} + 1)}{2}$

Step 7.5.4

Cancel the common factors.

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Step 7.5.4.1

Rewrite $2$ as $1 (2)$ .

$x = \frac{1 (- \sqrt{(- 2 y + 7) (2 y + 9)} + 1)}{1 (2)}$

Step 7.5.4.2

Cancel the common factor.

$x = \frac{1 (- \sqrt{(- 2 y + 7) (2 y + 9)} + 1)}{1 \cdot 2}$

Step 7.5.4.3

Rewrite the expression.

$x = \frac{- \sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

Step 7.6

Factor $- 1$ out of $- \sqrt{(- 2 y + 7) (2 y + 9)}$ .

$x = \frac{- (\sqrt{(- 2 y + 7) (2 y + 9)}) + 1}{2}$

Step 7.7

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

$x = \frac{- (\sqrt{(- 2 y + 7) (2 y + 9)}) - 1 \cdot - 1}{2}$

Step 7.8

Factor $- 1$ out of $- (\sqrt{(- 2 y + 7) (2 y + 9)}) - 1 (- 1)$ .

$x = \frac{- (\sqrt{(- 2 y + 7) (2 y + 9)} - 1)}{2}$

Step 7.9

Rewrite $- (\sqrt{(- 2 y + 7) (2 y + 9)} - 1)$ as $- 1 (\sqrt{(- 2 y + 7) (2 y + 9)} - 1)$ .

$x = \frac{- 1 (\sqrt{(- 2 y + 7) (2 y + 9)} - 1)}{2}$

Step 7.10

Move the negative in front of the fraction.

$x = - \frac{\sqrt{(- 2 y + 7) (2 y + 9)} - 1}{2}$

Step 8

The final answer is the combination of both solutions.

$x = \frac{\sqrt{(- 2 y + 7) (2 y + 9)} + 1}{2}$

$x = - \frac{\sqrt{(- 2 y + 7) (2 y + 9)} - 1}{2}$