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

Question

(
𝑥
+
16
)
2
9
=
7
.(1 point)
{}

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