Solve (x-5)^2=22

$$( x - 5 ) ^ { 2 } = 22$$

Solve for x

$$x=\sqrt{22}+5\approx 9.69041576$$

$$x=5-\sqrt{22}\approx 0.30958424$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-5=\sqrt{22} x-5=-\sqrt{22}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{22}-\left(-5\right) x-5-\left(-5\right)=-\sqrt{22}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{22}-\left(-5\right) x=-\sqrt{22}-\left(-5\right)$$

Subtract -5 from \sqrt{22}.

$$x=\sqrt{22}+5$$

Subtract -5 from -\sqrt{22}.

$$x=5-\sqrt{22}$$

The equation is now solved.

$$x=\sqrt{22}+5 x=5-\sqrt{22}$$