Question

complete the square to identify the two values that solve the following quadratic equation: x^2+8x=9.(1 point)

Answer 1

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

1. **Move the constant to the other side**:
\[
x^2 + 8x - 9 = 0.
\]

2. **Add \((\frac{b}{2})^2\)** to both sides. Here, \(b = 8\):
\[
\left(\frac{8}{2}\right)^2 = 4^2 = 16.
\]
Now we add 16 to both sides:
\[
x^2 + 8x + 16 = 9 + 16.
\]

3. **Simplify**:
\[
x^2 + 8x + 16 = 25.
\]

4. **Factor the left side**:
\[
(x + 4)^2 = 25.
\]

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

6. **Solve for \(x\)**:
- For the positive case:
\[
x + 4 = 5 \implies x = 5 - 4 = 1.
\]
- For the negative case:
\[
x + 4 = -5 \implies x = -5 - 4 = -9.
\]

Thus, the two values that solve the equation \(x^2 + 8x = 9\) are:
\[
\boxed{1} \quad \text{and} \quad \boxed{-9}.
\]