Question

Complete the square to identify the two values that solve the following quadratic equation: x2+8x=9
. Enter the two solutions separated by a comma.(1 point)
x=

Answer 1

To solve the quadratic equation \( x^2 + 8x = 9 \) by completing the square, we first rewrite the equation in a standard form:

1. Subtract 9 from both sides:
\[
x^2 + 8x - 9 = 0
\]

2. Now, focus on completing the square for the expression \( x^2 + 8x \).

- Take the coefficient of \( x \), which is \( 8 \), divide it by \( 2 \) to get \( 4 \), and then square it to get \( 16 \).

3. Add and subtract \( 16 \) inside the equation:
\[
x^2 + 8x + 16 - 16 - 9 = 0
\]
This simplifies to:
\[
(x + 4)^2 - 25 = 0
\]

4. Rearranging the equation gives:
\[
(x + 4)^2 = 25
\]

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

6. Solve for \( x \):
- For \( x + 4 = 5 \):
\[
x = 5 - 4 = 1
\]
- For \( x + 4 = -5 \):
\[
x = -5 - 4 = -9
\]

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

The final answer is:
\[
x = 1, -9
\]