Question

omplete the square to identify the two values that solve the following quadratic equation: x2+8x=9 .(1 point)

Answer 1

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

1. Start with the equation:
\[
x^2 + 8x - 9 = 0
\]

2. Move the constant to the other side:
\[
x^2 + 8x = 9
\]

3. To complete the square, take the coefficient of \( x \) (which is 8), divide it by 2, and square it. The calculation is:
\[
\left(\frac{8}{2}\right)^2 = 4^2 = 16
\]

4. Add and subtract this value (16) to the left side of the equation:
\[
x^2 + 8x + 16 - 16 = 9
\]

5. Simplifying gives:
\[
(x + 4)^2 - 16 = 9
\]

6. Now, move the \(-16\) to the right side:
\[
(x + 4)^2 = 9 + 16
\]
\[
(x + 4)^2 = 25
\]

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

8. 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 equation \( x^2 + 8x = 9 \) are:
\[
\boxed{1} \text{ and } \boxed{-9}
\]