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

Question

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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:

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

2. Solve for \(x\):

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

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

   \[ \sqrt{51} \approx 7.14 \quad (\text{rounded to the nearest hundredth}) \]

4. Therefore, the two solutions for \(x\) are:

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

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

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

\[ \boxed{13.14} \quad \text{and} \quad \boxed{-1.14} \]