Question

Complete the square to solve the equation below (check all that apply)

Answer 1

A and D

Explanation:

We have to create a perfect square. To make x^2+bx+c into a perfect square, c has to be (b/2)^2. In this case, b is -10. so, c has to be (-10/2)^2, which is 25. To make the left hand side 25, we would have to add 30 to both sides.

This leads to a new equation:

x^2 - 10x + 25 = 9+30

x^2 - 10x + 25 = 39

Now, we can change the left hand side to a perfect square.

(x-5)^2 = 39. (the -5 is b/2)

Then we square root both sides;

x-5 = +/- sqrt39. (When you square root an expression, remember that you need to include both the positive AND negative)

x = 5-sqrt39 or 5+sqrt39