Question

Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?

[p and q are integers] (5 points)
Step 1x2 + 8x + 15 - 1 = 0 - 1
Step 2x2 + 8x + 14 = -1
Step 3(x + 4)2 = -1
Step 1x2 + 8x + 15 - 2 - 0 - 2
Step 2x² + 8x + 13 = -2
Step 3(x + 4)2 = -2
Step 1x2 + 8x + 15 + 1 = 0 + 1
Step 2x2 + 8x + 16 = 1
Step 3(x + 4)2 = 1
Step 1x2 + 8x + 15 + 2 = 0 + 2
Step 2x2 + 8x + 17 = 20
Step 3(x + 4)2 = 2

Answer 1

Step 1 x2 + 8x + 15 + 1 = 0 + 1

Step 2 x2 + 8x + 16 = 1

Step 3 (x + 4)2 = 1

Explanation:

took the test

Answer 2

Step 1: x^2 + 8x + 15 + 1 = 0 + 1

Step 2: x^2 + 8x + 16 = 1

Step 3: (x + 4)^2 = 1

Explanation:

You want the constant on the left to be the square of half the x-coefficient.

(8/2)^2 = 4^2 = 16

You already have a constant that is 15, so you need to add 1 to both sides of the equation. That is the Step 1 shown here. Step 2 is simplifying the result of Step 1. Step 3 is rewriting the trinomial as the square of a binomial.