Finite Math Examples

${(x - 3)}^{2} + {(y - 5)}^{2} = r^{2}$

Step 1

Subtract $r^{2}$ from both sides of the equation.

${(x - 3)}^{2} + {(y - 5)}^{2} - r^{2} = 0$

Step 2

Simplify ${(x - 3)}^{2} + {(y - 5)}^{2} - r^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$(x - 3) (x - 3) + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$x (x - 3) - 3 (x - 3) + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 5)}^{2} - r^{2} = 0$

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 $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.3.1.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.3.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.3.2

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 6 x + 9 + {(y - 5)}^{2} - r^{2} = 0$

Step 2.1.4

Rewrite ${(y - 5)}^{2}$ as $(y - 5) (y - 5)$ .

$x^{2} - 6 x + 9 + (y - 5) (y - 5) - r^{2} = 0$

Step 2.1.5

Expand $(y - 5) (y - 5)$ using the FOIL Method.

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Step 2.1.5.1

Apply the distributive property.

$x^{2} - 6 x + 9 + y (y - 5) - 5 (y - 5) - r^{2} = 0$

Step 2.1.5.2

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 5 - 5 (y - 5) - r^{2} = 0$

Step 2.1.5.3

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5 - r^{2} = 0$

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 $y$ .

$x^{2} - 6 x + 9 + y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5 - r^{2} = 0$

Step 2.1.6.1.2

Move $- 5$ to the left of $y$ .

$x^{2} - 6 x + 9 + y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5 - r^{2} = 0$

Step 2.1.6.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} - 6 x + 9 + y^{2} - 5 y - 5 y + 25 - r^{2} = 0$

Step 2.1.6.2

Subtract $5 y$ from $- 5 y$ .

$x^{2} - 6 x + 9 + y^{2} - 10 y + 25 - r^{2} = 0$

Step 2.2

Add $9$ and $25$ .

$x^{2} - 6 x + y^{2} - 10 y + 34 - r^{2} = 0$

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 $a = 1$ , $b = - 6$ , and $c = y^{2} - 10 y + 34 - r^{2}$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot (y^{2} - 10 y + 34 - r^{2}))}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 5.1.3

Apply the distributive property.

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} - 4 (- 10 y) - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 5.1.4

Simplify.

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Step 5.1.4.1

Multiply $- 10$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 5.1.4.2

Multiply $- 4$ by $34$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 - 4 (- r^{2})}}{2 \cdot 1}$

Step 5.1.4.3

Multiply $- 1$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.5

Subtract $136$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4 y^{2} + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6

Rewrite $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ in a factored form.

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Step 5.1.6.1

Factor $4$ out of $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ .

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Step 5.1.6.1.1

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

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6.1.2

Factor $4$ out of $40 y$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6.1.3

Factor $4$ out of $- 100$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6.1.4

Factor $4$ out of $4 (- y^{2}) + 4 (10 y)$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6.1.5

Factor $4$ out of $4 (- y^{2} + 10 y) + 4 \cdot - 25$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25) + 4 r^{2}}}{2 \cdot 1}$

Step 5.1.6.1.6

Factor $4$ out of $4 (- y^{2} + 10 y - 25) + 4 r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25 + r^{2})}}{2 \cdot 1}$

Step 5.1.6.2

Rewrite $y^{2} - 10 y + 25$ as ${(y - 5)}^{2}$ .

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Step 5.1.6.2.1

Rewrite $25$ as $5^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 10 y + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 5.1.6.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 y = 2 \cdot y \cdot 5$

Step 5.1.6.2.3

Rewrite the polynomial.

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 2 \cdot y \cdot 5 + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 5.1.6.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 5$ .

$x = \frac{6 \pm \sqrt{4 (- {(y - 5)}^{2} + r^{2})}}{2 \cdot 1}$

Step 5.1.6.3

Reorder $- {(y - 5)}^{2}$ and $r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (r^{2} - {(y - 5)}^{2})}}{2 \cdot 1}$

Step 5.1.6.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = y - 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - (y - 5)))}}{2 \cdot 1}$

Step 5.1.6.5

Simplify.

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Step 5.1.6.5.1

Apply the distributive property.

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 5.1.6.5.2

Multiply $- 1$ by $- 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

$x = \frac{6 \pm \sqrt{4 (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 5.1.7

Rewrite $4 (r + y - 5) (r - y + 5)$ as $2^{2} ((r + y - 5) (r - y + 5))$ .

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Step 5.1.7.1

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm \sqrt{2^{2} (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 5.1.7.2

Add parentheses.

$x = \frac{6 \pm \sqrt{2^{2} ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 5.1.8

Pull terms out from under the radical.

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$

Step 5.3

Simplify $\frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$ .

$x = 3 \pm \sqrt{(r + y - 5) (r - y + 5)}$

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 $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 6.1.3

Apply the distributive property.

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} - 4 (- 10 y) - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 6.1.4

Simplify.

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Step 6.1.4.1

Multiply $- 10$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 6.1.4.2

Multiply $- 4$ by $34$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 - 4 (- r^{2})}}{2 \cdot 1}$

Step 6.1.4.3

Multiply $- 1$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.5

Subtract $136$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4 y^{2} + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6

Rewrite $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ in a factored form.

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Step 6.1.6.1

Factor $4$ out of $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ .

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Step 6.1.6.1.1

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

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6.1.2

Factor $4$ out of $40 y$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6.1.3

Factor $4$ out of $- 100$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6.1.4

Factor $4$ out of $4 (- y^{2}) + 4 (10 y)$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6.1.5

Factor $4$ out of $4 (- y^{2} + 10 y) + 4 \cdot - 25$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25) + 4 r^{2}}}{2 \cdot 1}$

Step 6.1.6.1.6

Factor $4$ out of $4 (- y^{2} + 10 y - 25) + 4 r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25 + r^{2})}}{2 \cdot 1}$

Step 6.1.6.2

Rewrite $y^{2} - 10 y + 25$ as ${(y - 5)}^{2}$ .

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Step 6.1.6.2.1

Rewrite $25$ as $5^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 10 y + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 6.1.6.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 y = 2 \cdot y \cdot 5$

Step 6.1.6.2.3

Rewrite the polynomial.

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 2 \cdot y \cdot 5 + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 6.1.6.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 5$ .

$x = \frac{6 \pm \sqrt{4 (- {(y - 5)}^{2} + r^{2})}}{2 \cdot 1}$

Step 6.1.6.3

Reorder $- {(y - 5)}^{2}$ and $r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (r^{2} - {(y - 5)}^{2})}}{2 \cdot 1}$

Step 6.1.6.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = y - 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - (y - 5)))}}{2 \cdot 1}$

Step 6.1.6.5

Simplify.

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Step 6.1.6.5.1

Apply the distributive property.

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 6.1.6.5.2

Multiply $- 1$ by $- 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

$x = \frac{6 \pm \sqrt{4 (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 6.1.7

Rewrite $4 (r + y - 5) (r - y + 5)$ as $2^{2} ((r + y - 5) (r - y + 5))$ .

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Step 6.1.7.1

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm \sqrt{2^{2} (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 6.1.7.2

Add parentheses.

$x = \frac{6 \pm \sqrt{2^{2} ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 6.1.8

Pull terms out from under the radical.

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$

Step 6.3

Simplify $\frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$ .

$x = 3 \pm \sqrt{(r + y - 5) (r - y + 5)}$

Step 6.4

Change the $\pm$ to $+$ .

$x = 3 + \sqrt{(r + y - 5) (r - y + 5)}$

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 $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot (y^{2} - 10 y + 34 - r^{2})}}{2 \cdot 1}$

Step 7.1.3

Apply the distributive property.

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} - 4 (- 10 y) - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 7.1.4

Simplify.

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Step 7.1.4.1

Multiply $- 10$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 4 \cdot 34 - 4 (- r^{2})}}{2 \cdot 1}$

Step 7.1.4.2

Multiply $- 4$ by $34$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 - 4 (- r^{2})}}{2 \cdot 1}$

Step 7.1.4.3

Multiply $- 1$ by $- 4$ .

$x = \frac{6 \pm \sqrt{36 - 4 y^{2} + 40 y - 136 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.5

Subtract $136$ from $36$ .

$x = \frac{6 \pm \sqrt{- 4 y^{2} + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6

Rewrite $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ in a factored form.

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Step 7.1.6.1

Factor $4$ out of $- 4 y^{2} + 40 y - 100 + 4 r^{2}$ .

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Step 7.1.6.1.1

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

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 40 y - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6.1.2

Factor $4$ out of $40 y$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) - 100 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6.1.3

Factor $4$ out of $- 100$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2}) + 4 (10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6.1.4

Factor $4$ out of $4 (- y^{2}) + 4 (10 y)$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y) + 4 \cdot - 25 + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6.1.5

Factor $4$ out of $4 (- y^{2} + 10 y) + 4 \cdot - 25$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25) + 4 r^{2}}}{2 \cdot 1}$

Step 7.1.6.1.6

Factor $4$ out of $4 (- y^{2} + 10 y - 25) + 4 r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- y^{2} + 10 y - 25 + r^{2})}}{2 \cdot 1}$

Step 7.1.6.2

Rewrite $y^{2} - 10 y + 25$ as ${(y - 5)}^{2}$ .

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Step 7.1.6.2.1

Rewrite $25$ as $5^{2}$ .

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 10 y + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 7.1.6.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 y = 2 \cdot y \cdot 5$

Step 7.1.6.2.3

Rewrite the polynomial.

$x = \frac{6 \pm \sqrt{4 (- (y^{2} - 2 \cdot y \cdot 5 + 5^{2}) + r^{2})}}{2 \cdot 1}$

Step 7.1.6.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 5$ .

$x = \frac{6 \pm \sqrt{4 (- {(y - 5)}^{2} + r^{2})}}{2 \cdot 1}$

Step 7.1.6.3

Reorder $- {(y - 5)}^{2}$ and $r^{2}$ .

$x = \frac{6 \pm \sqrt{4 (r^{2} - {(y - 5)}^{2})}}{2 \cdot 1}$

Step 7.1.6.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = y - 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - (y - 5)))}}{2 \cdot 1}$

Step 7.1.6.5

Simplify.

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Step 7.1.6.5.1

Apply the distributive property.

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 7.1.6.5.2

Multiply $- 1$ by $- 5$ .

$x = \frac{6 \pm \sqrt{4 ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

$x = \frac{6 \pm \sqrt{4 (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 7.1.7

Rewrite $4 (r + y - 5) (r - y + 5)$ as $2^{2} ((r + y - 5) (r - y + 5))$ .

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Step 7.1.7.1

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm \sqrt{2^{2} (r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 7.1.7.2

Add parentheses.

$x = \frac{6 \pm \sqrt{2^{2} ((r + y - 5) (r - y + 5))}}{2 \cdot 1}$

Step 7.1.8

Pull terms out from under the radical.

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$x = \frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$

Step 7.3

Simplify $\frac{6 \pm 2 \sqrt{(r + y - 5) (r - y + 5)}}{2}$ .

$x = 3 \pm \sqrt{(r + y - 5) (r - y + 5)}$

Step 7.4

Change the $\pm$ to $-$ .

$x = 3 - \sqrt{(r + y - 5) (r - y + 5)}$

Step 8

The final answer is the combination of both solutions.

$x = 3 + \sqrt{(r + y - 5) (r - y + 5)}$

$x = 3 - \sqrt{(r + y - 5) (r - y + 5)}$