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

Question

(
𝑥
−
6
)
2
=
51
.(1 point)
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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. Isolate \(x\): \[ x = 6 \pm \sqrt{51} \]

3. Calculate \(\sqrt{51}\). The approximate value of \(\sqrt{51}\) is about 7.14 (rounded to two decimal places).

4. Find the two values for \(x\): \[ x = 6 + \sqrt{51} \quad \text{and} \quad x = 6 - \sqrt{51} \]

   • For \(x = 6 + \sqrt{51}\): \[ x \approx 6 + 7.14 = 13.14 \]
   • For \(x = 6 - \sqrt{51}\): \[ x \approx 6 - 7.14 = -1.14 \]

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

In summary, the solutions rounded to the nearest hundredth are: \[ { 13.14, -1.14 } \]