Question

Complete the square to identify the two values that solve the following quadratic equation: x^2 + 8x = 9

Answer 1

To complete the square for the equation \( x^2 + 8x = 9 \), follow these steps:

1. Move the constant term to the right side of the equation:
\[
x^2 + 8x - 9 = 0
\]

2. Rewrite the equation focusing on the left side:
\[
x^2 + 8x = 9
\]

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

4. Add 16 to both sides of the equation:
\[
x^2 + 8x + 16 = 9 + 16
\]
\[
x^2 + 8x + 16 = 25
\]

5. Now, the left side can be factored as a perfect square:
\[
(x + 4)^2 = 25
\]

6. Take the square root of both sides:
\[
x + 4 = \pm 5
\]

7. Solve for \( x \):
- For \( x + 4 = 5 \):
\[
x = 5 - 4 = 1
\]

- For \( x + 4 = -5 \):
\[
x = -5 - 4 = -9
\]

Thus, the two values that solve the quadratic equation \( x^2 + 8x = 9 \) are \( x = 1 \) and \( x = -9 \).