Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x−6)^2=51.(1 point)

Answer 1

To solve the quadratic equation \((x - 6)^2 = 51\), we can use the square root method. Here are the steps:

1. Take the square root of both sides of the equation:

\[
x - 6 = \pm \sqrt{51}
\]

2. Calculate \(\sqrt{51}\):

\[
\sqrt{51} \approx 7.14 \quad (\text{rounded to two decimal places})
\]

3. Now, we have two equations to solve:

\[
x - 6 = 7.14 \quad \text{and} \quad x - 6 = -7.14
\]

4. Solve the first equation:

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

5. Solve the second equation:

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

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

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