Question

Complete the square x^2-12x+32=4​

Answer 1

Step 1) Move all constants to the right side, leaving all of the terms with variables on the left side

x^2 - 12x = -28

Step 2) Find a number that would create a perfect square trinomial on the left side. For this problem, that would be 36. So, we need to add 36 to the left and right sides.

x^2 - 12x + 36 = -28 + 36

x^2 - 12x + 36 = 8

Step 3) Rewrite the perfect square trinomial on the left, so it only has two terms (becomes the square of itself)

(x - 6)^2 = 8

Step 4) Take the square root of both sides - remember that it is plus/minus because of the square!

x - 6 = ±
`√(8)`

x - 6 = ±
`2√(2)`

Step 5) Find the two solutions of x

x = 6 +
`2√(2)`

x = -6 +
`2√(2)`

Hope this helps! :)