Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)29=7
(
𝑥
+
16
)
2
9
=
7
.(1 point)
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Answer 1

To solve the quadratic equation \((x + 16)^{2} = 7\) using square roots, follow these steps:

1. **Move the constant to one side:**
\[
(x + 16)^{2} = 7
\]

2. **Take the square root of both sides:**
\[
x + 16 = \pm \sqrt{7}
\]

3. **Isolate \(x\):**
\[
x = -16 \pm \sqrt{7}
\]

4. **Calculate the two possible values for \(x\):**
\[
x_1 = -16 + \sqrt{7}
\]
\[
x_2 = -16 - \sqrt{7}
\]

5. **Evaluate \(\sqrt{7} \approx 2.64575\):**
\[
x_1 = -16 + 2.64575 \approx -13.35425 \quad \text{(rounded to -13.35)}
\]
\[
x_2 = -16 - 2.64575 \approx -18.64575 \quad \text{(rounded to -18.65)}
\]

So the two solutions to the equation \((x + 16)^{2} = 7\) are:
\[
x \approx -13.35 \quad \text{and} \quad x \approx -18.65
\]

**Final answers:**
\[
x_1 \approx -13.35, \quad x_2 \approx -18.65
\]