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

Answer 1

To solve the quadratic equation, we will first take the square root of both sides of the equation:

√((x-6)^2) = √51

Simplifying the left side:

x - 6 = ±√51

Next, we will isolate x by adding 6 to both sides:

x = 6 ± √51

Rounding to the nearest hundredth:

x ≈ 6 + 7.14 ≈ 13.14 or x ≈ 6 - 7.14 ≈ -1.14

Therefore, the solutions to the quadratic equation (x-6)^2 = 51 are approximately x = 13.14 and x = -1.14.