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

1 Answer

Answer:

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#