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

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

2. Solve for \(x\) by isolating it:
\[
x = 6 \pm \sqrt{51}
\]

3. Calculate \(\sqrt{51}\):
\[
\sqrt{51} \approx 7.14
\]

4. Now substitute back to find the two possible values of \(x\):
\[
x = 6 + 7.14 \quad \text{and} \quad x = 6 - 7.14
\]

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

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

Thus, the solutions to the equation \((x - 6)^2 = 51\) are approximately:
\[
x \approx 13.14 \quad \text{and} \quad x \approx -1.14
\]