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

3. Now, rewrite the equation: \[ x - 6 = 7.14 \quad \text{or} \quad x - 6 = -7.14 \]

4. Solve for \(x\) in both cases:

   • For \(x - 6 = 7.14\): \[ x = 7.14 + 6 = 13.14 \]

   • For \(x - 6 = -7.14\): \[ x = -7.14 + 6 = -1.14 \]

5. Final solutions: \[ x \approx 13.14 \quad \text{or} \quad x \approx -1.14 \]

So the solutions are \(x \approx 13.14\) and \(x \approx -1.14\).