Complete the Square x^2+12x-69

$x^{2} + 12 x - 69$

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = 12, c = - 69$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{12}{2 (1)}$

Cancel the common factor of $12$ and $2$ .

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Factor $2$ out of $12$ .

$d = \frac{2 \cdot 6}{2 \cdot 1}$

Cancel the common factors.

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Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot 6}{2 (1)}$

Cancel the common factor.

$d = \frac{2 \cdot 6}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{6}{1}$

Divide $6$ by $1$ .

$d = 6$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Simplify each term.

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Raise $12$ to the power of $2$ .

$e = - 69 - \frac{144}{4 (1)}$

Multiply $4$ by $1$ .

$e = - 69 - \frac{144}{4}$

Divide $144$ by $4$ .

$e = - 69 - 1 \cdot 36$

Multiply $- 1$ by $36$ .

$e = - 69 - 36$

Subtract $36$ from $- 69$ .

$e = - 105$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(x + 6)}^{2} - 105$

Complete the Square x^2+12x-69

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