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, we can first take the square root of both sides:

$\sqrt{(x-6)^2}=\sqrt{51}$

$x-6=\pm\sqrt{51}$

Now, we can add 6 to both sides to isolate $x$:

$x=6\pm\sqrt{51}$

Rounded to the nearest hundredth, the solutions are:

$x\approx6+\sqrt{51}\approx6+7.14\approx\boxed{13.14}$

$x\approx6-\sqrt{51}\approx6-7.14\approx\boxed{-1.14}$