Question

Ite Solve the following quadratic equation using square rootsRound to the nearest hundredth if necessary: ((x + 16) ^ 2)/9 = 7 (1 point)

Answer 1

To solve the quadratic equation \(\frac{(x + 16)^2}{9} = 7\), we can follow these steps:

1. **Multiply both sides by 9** to eliminate the fraction:
\[
(x + 16)^2 = 63
\]

2. **Take the square root of both sides**:
\[
x + 16 = \pm \sqrt{63}
\]

3. **Calculate \(\sqrt{63}\)**:
\[
\sqrt{63} \approx 7.94 \quad (\text{rounded to the nearest hundredth})
\]

4. **Set up the equations** from the square root:
\[
x + 16 = 7.94 \quad \text{or} \quad x + 16 = -7.94
\]

5. **Solve for \(x\)** in both cases:
- For \(x + 16 = 7.94\):
\[
x = 7.94 - 16 = -8.06
\]

- For \(x + 16 = -7.94\):
\[
x = -7.94 - 16 = -23.94
\]

Thus, the solutions to the quadratic equation are:
\[
x \approx -8.06 \quad \text{and} \quad x \approx -23.94
\]