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 1 x2 + 8x + 15 − 2 = 0 − 2 Step 2 x2 + 8x + 13 = −2 Step 3 (x + 4)2 = −2 Step 1 x2 + 8x + 15 − 1 = 0 − 1 Step 2 x2 + 8x + 14 = −1 Step 3 (x + 4)2 = −1 Step 1 x2 + 8x + 15 + 2 = 0 + 2 Step 2 x2 + 8x + 17 = 2 Step 3 (x + 4)2 = 2 Step 1 x2 + 8x + 15 + 1 = 0 + 1 Step 2 x2 + 8x + 16 = 1 Step 3 (x + 4)2 = 1

Answer 1

The correct steps are:

start with

`x^2+8x+15=0`

Add 1 to both sides:

`x^2+8x+16=1`

The left hand side is a perfect square:

`(x+4)^2=1`

Answer 2

Option D

Explanation:

The given expression is x² + 8x + 15 = 0

We have to solve it further to transform into the form ( x - p )² = q

x² + 8x + 15 = 0

[ x² + 8x + 15 ] + 1 = 0 + 1

x² + 8x + 16 = 1

( x + 4 )² = 1

Option D is the answer.