Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x−6)^2=51
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:
$x\approx6+\sqrt{51}\approx6+7.14\approx\boxed{13.14}$
$x\approx6-\sqrt{51}\approx6-7.14\approx\boxed{-1.14}$