Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x−6)2=51

Answer 1

To solve the equation \((x - 6)^2 = 51\) using square roots, follow these steps:

1. **Take the square root of both sides**:
\[
x - 6 = \pm \sqrt{51}
\]

2. **Calculate \(\sqrt{51}\)**:
\[
\sqrt{51} \approx 7.14 \quad (\text{to two decimal places})
\]

3. **Now, rewrite the equation**:
\[
x - 6 = 7.14 \quad \text{or} \quad x - 6 = -7.14
\]

4. **Solve for \(x\)** in both cases:

- For \(x - 6 = 7.14\):
\[
x = 7.14 + 6 = 13.14
\]

- For \(x - 6 = -7.14\):
\[
x = -7.14 + 6 = -1.14
\]

5. **Final solutions**:
\[
x \approx 13.14 \quad \text{or} \quad x \approx -1.14
\]

So the solutions are \(x \approx 13.14\) and \(x \approx -1.14\).