Question

Rewrite x2 − 8x + 13 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.

Answer 1

You’ll need to complete the square.

Take the x term (-8x). It’s coefficient is -8. Divide this by 2 and square it. (-8/2)^2 = 16

Then add 16 to both sides of the original equation

(x^2 -8x + 16) + 13 = 16

Notice how the expression in parentheses is a perfect square trinomial. Factor the trinomial, the subtract 13 from both sides to isolate the factored expression on the left. You should end up with an equation in the form (x-a)^2 = b for which you can identify your a and b values.