Question

Solve using completing the square x^2 – 8x + 16 = 25

Answer 1

First we need to factor the left side. Since it is a perfect square (as is the process with completing the square, we know we can take half of the middle number along with x to be in the two parenthesis.

(x - 4)(x - 4) = 25

Now we simplify to show it as a square.

(x - 4)^2 = 25

Next we take the square root of both sides

x - 4 = +/- 5

Note that we have plus or minus 5. This is because either square would give us positive 25. Now we add 4 to both sides

x = 4 +/- 5

4 + 5 = 9

4 - 5 = -1