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 \(\sqrt{51}\):**

The square root of 51 is approximately \(7.14\) (when rounded to the nearest hundredth).

3. **Set up both equations:**

\[
x - 6 = \sqrt{51} \quad \text{and} \quad x - 6 = -\sqrt{51}
\]

4. **Solve the first equation:**

\[
x - 6 = 7.14
\]
\[
x = 7.14 + 6
\]
\[
x \approx 13.14
\]

5. **Solve the second equation:**

\[
x - 6 = -7.14
\]
\[
x = -7.14 + 6
\]
\[
x \approx -1.14
\]

Thus, the solutions to the equation \((x - 6)^2 = 51\) are:

\[
x \approx 13.14 \quad \text{and} \quad x \approx -1.14
\]