Question

1.

What number should be added to the expression x^2 + 2x to change it into a perfect square trinomial?

2
What number should be added to the expression x^2+12x to change it into a perfect square trinomial?

3
Which statement describes the first step to solve the equation by completing the square?

3x^2+18x=21

Answer 1

1. Add 1

2. Add 36

3. Divide both sides by 3

Explanation:

When you are trying to "complete the square" There's going to be an x^2 term and also an x term. Take the number beside the x, cut it in half, and then square it.

1. 2 is beside the x. Cut 2 in half, that's 1, 1^2 is just 1. So add 1.

x^2 + 2x + 1 is a perfect square trinomial. It equals (x + 1)^2

2. 12 is beside the x. Cut 12 in half, that's 6, 6^2 is 36. So add 36.

x^2 + 12x + 36 is a perfect square trinomial. It equals (x + 6)^2

3. In order to "complete the square" the x^2 term must not have a coefficient (a number beside it) So we divide thru on both sides by 3 to get rid of the 3 in front of the x^2 term.