Solve (x-7)^2=7

$$( x - 7 ) ^ { 2 } = 7$$

Solve for x

$$x=\sqrt{7}+7\approx 9.645751311$$

$$x=7-\sqrt{7}\approx 4.354248689$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-7=\sqrt{7} x-7=-\sqrt{7}$$

Add 7 to both sides of the equation.

$$x-7-\left(-7\right)=\sqrt{7}-\left(-7\right) x-7-\left(-7\right)=-\sqrt{7}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$x=\sqrt{7}-\left(-7\right) x=-\sqrt{7}-\left(-7\right)$$

Subtract -7 from \sqrt{7}.

$$x=\sqrt{7}+7$$

Subtract -7 from -\sqrt{7}.

$$x=7-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+7 x=7-\sqrt{7}$$