# How do you solve x^2 + 12 = (x - 4)^2?

First square the term on the right side, then combine like terms, and you'll get to $x = \frac{1}{2}$

#### Explanation:

To solve this, we first need to square the $x - 4$ term, then combine like terms across the entire equation. Like this:

${x}^{2} + 12 = {\left(x - 4\right)}^{2}$
${x}^{2} + 12 = {x}^{2} - 8 x + 16$

We can subtract ${x}^{2} - 8 x$ from both sides (to move the x terms to the left side of the equation):

$8 x + 12 = 16$

We can now subtract 12 from both sides (to move the constants to the right side of the equation - and we could have done both this and the last step as one but I broke it out for clarity):

$8 x = 4$

Let's divide both sides by 8 to solve for x:

$x = \frac{4}{8} = \frac{1}{2}$