Question

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

Answer 1

First square the term on the right side, then combine like terms, and you'll get to `x=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=(x-4)^2`
`x^2+12=x^2-8x+16`

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

`8x+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):

`8x=4`

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

`x=4/8=1/2`