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]


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 + 13 = −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

Step 1 x2 + 8x + 15 + 2 = 0 + 2
Step 2 x2 + 8x + 17 = 2
Step 3 (x + 4)2 = 2

Answer 1

The third approach is the correct approach. The reason for this is because what you’re trying to get requires a function with a perfect, and 16 is the only value with an integer square root. I’d recommend attempting to undo the last step yourself and seeing what values you’ll get, as you’ll notice that when you’re undoing (x + 4)^2, there is only one proper way to approach it.