Solve (x-5)^2=7

$$( x - 5 ) ^ { 2 } = 7$$

Solve for x

$$x=\sqrt{7}+5\approx 7.645751311$$

$$x=5-\sqrt{7}\approx 2.354248689$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-5=\sqrt{7} x-5=-\sqrt{7}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{7}-\left(-5\right) x-5-\left(-5\right)=-\sqrt{7}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{7}-\left(-5\right) x=-\sqrt{7}-\left(-5\right)$$

Subtract -5 from \sqrt{7}.

$$x=\sqrt{7}+5$$

Subtract -5 from -\sqrt{7}.

$$x=5-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+5 x=5-\sqrt{7}$$