Question

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

x=

Answer 1

there is not one answer?

Answer 2

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

1. **Rearrange the equation** so that the constant is on the right side:
\[
x^2 + 8x - 9 = 0
\]

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

3. **Complete the square** on the left side. To do this, take half of the coefficient of \( x \) (which is 8), square it, and add it to both sides:
- Half of 8 is 4, and \( 4^2 = 16 \).
\[
x^2 + 8x + 16 = 9 + 16
\]

4. **Simplify both sides**:
\[
(x + 4)^2 = 25
\]

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

6. **Solve for \( x \)** by isolating it:
- First solution:
\[
x + 4 = 5 \quad \Rightarrow \quad x = 5 - 4 = 1
\]
- Second solution:
\[
x + 4 = -5 \quad \Rightarrow \quad x = -5 - 4 = -9
\]

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

Answer 3

The quadratic equation \(x^2 + 8x = 9\) actually has two solutions because it is a second-degree polynomial equation.

After completing the square, we found that:
\[
(x + 4)^2 = 25
\]
Taking the square root gives us two cases:
1. \(x + 4 = 5\)
2. \(x + 4 = -5\)

Solving these gives:
1. From \(x + 4 = 5\):
\[
x = 1
\]
2. From \(x + 4 = -5\):
\[
x = -9
\]

Thus, the two solutions are \(x = 1\) and \(x = -9\).

If you need just one answer, you can refer to either \(x = 1\) or \(x = -9\), but keep in mind that both values are solutions to the equation. If you're looking for a specific format or context, please let me know!