solve the following quadratic equation using square roots. round to the nearest hundredth if necessary: (x-6)^2 = 51
To solve the quadratic equation (x-6)^2 = 51, we need to take the square root of both sides of the equation to isolate x.
Taking the square root of both sides, we get:
x - 6 = ±√51
Now, we can solve this equation for x:
1. x - 6 = √51
Adding 6 to both sides:
x = √51 + 6
2. x - 6 = -√51
Adding 6 to both sides:
x = -√51 + 6
Now, let's substitute the value of √51 with its approximate decimal value:
√51 ≈ 7.14
Hence, rounding to the nearest hundredth, the solutions to the quadratic equation (x-6)^2 = 51 are:
x = 7.14 + 6 ≈ 13.14
x = -7.14 + 6 ≈ -1.14