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

Question

.(1 point)

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. Simplify the square root: \[ x - 6 = \pm \sqrt{51} \] Since \(\sqrt{51} \approx 7.14\) (rounded to two decimal places), we have: \[ x - 6 = \pm 7.14 \]

3. Now, solve for \(x\) by adding 6 to both sides for both cases:

   Case 1: \(x - 6 = 7.14\) \[ x = 7.14 + 6 = 13.14 \]

   Case 2: \(x - 6 = -7.14\) \[ x = -7.14 + 6 = -1.14 \]

4. Thus, the solutions to the equation are: \[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]

So the final answers are: \[ x \approx 13.14 \text{ and } x \approx -1.14 \]