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 \((x - 6)^2 = 51\), we'll first take the square root of both sides.

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

2. Next, solve for \(x\) by adding 6 to both sides: \[ x = 6 \pm \sqrt{51} \]

3. Now, we need to calculate \(\sqrt{51}\): \[ \sqrt{51} \approx 7.1414 \]

4. Therefore, we find the two possible values for \(x\): \[ x \approx 6 + 7.1414 \quad \text{and} \quad x \approx 6 - 7.1414 \]

   Calculating these:

   • For \(x \approx 6 + 7.1414\): \[ x \approx 13.1414 \]
   • For \(x \approx 6 - 7.1414\): \[ x \approx -1.1414 \]

5. Finally, rounding these values to the nearest hundredth: \[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]

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