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:

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