Question

When solving the equation x^2 - 8x - 7 = 0 by completing the square, which equation is a step in the process? Hint: After you complete the square, move constant to right side to rewrite in the form (x - p)2 = q and constant term sign will change.

A.
(x-8)² = 9

B.
(x-4)² = 9

C.
(x-8)² = 23

D.
(x-4)² = 23

Answer 1

To solve the equation \( x^2 - 8x - 7 = 0 \) by completing the square, let's follow the steps:

1. Start with the original equation:
\[
x^2 - 8x - 7 = 0
\]

2. Move the constant term to the right side:
\[
x^2 - 8x = 7
\]

3. To complete the square, we need to take the coefficient of \( x \), which is \(-8\), halve it, and square it:
\[
\left(-\frac{8}{2}\right)^2 = (-4)^2 = 16
\]

4. Add this square to both sides:
\[
x^2 - 8x + 16 = 7 + 16
\]
\[
x^2 - 8x + 16 = 23
\]

5. The left side now factors as:
\[
(x - 4)^2 = 23
\]

Thus, the equation after completing the square becomes:
\[
(x - 4)^2 = 23
\]

This corresponds to option **D**:
\[
\text{D. } (x - 4)^2 = 23
\]