Solve (x-6)^2=17

$$( x - 6 ) ^ { 2 } = 17$$

Solve for x

$$x=\sqrt{17}+6\approx 10.123105626$$

$$x=6-\sqrt{17}\approx 1.876894374$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-6=\sqrt{17} x-6=-\sqrt{17}$$

Add 6 to both sides of the equation.

$$x-6-\left(-6\right)=\sqrt{17}-\left(-6\right) x-6-\left(-6\right)=-\sqrt{17}-\left(-6\right)$$

Subtracting -6 from itself leaves 0.

$$x=\sqrt{17}-\left(-6\right) x=-\sqrt{17}-\left(-6\right)$$

Subtract -6 from \sqrt{17}.

$$x=\sqrt{17}+6$$

Subtract -6 from -\sqrt{17}.

$$x=6-\sqrt{17}$$

The equation is now solved.

$$x=\sqrt{17}+6 x=6-\sqrt{17}$$