Solve for x x^2+12x+36=0

$x^{2} + 12 x + 36 = 0$

Factor using the perfect square rule.

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Rewrite $36$ as $6^{2}$ .

$x^{2} + 12 x + 6^{2} = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot 6$

Simplify.

$2 a b = 12 x$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 6$ .

${(x + 6)}^{2} = 0$

Set the $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Solve for x x^2+12x+36=0

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