Solve for x x^2+36=12x

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

Step 1

Subtract $12 x$ from both sides of the equation.

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

Step 2

Factor using the perfect square rule.

Rearrange terms.

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

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

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

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

$12 x = 2 \cdot x \cdot 6$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 6 + 6^{2} = 0$

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

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

Step 3

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

$x - 6 = 0$

Step 4

Add $6$ to both sides of the equation.

$x = 6$