Solve (x-15)^2=45

$$( x - 15 ) ^ { 2 } = 45$$

Solve for x

$$x=3\sqrt{5}+15\approx 21.708203932$$

$$x=15-3\sqrt{5}\approx 8.291796068$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-15=3\sqrt{5} x-15=-3\sqrt{5}$$

Add 15 to both sides of the equation.

$$x-15-\left(-15\right)=3\sqrt{5}-\left(-15\right) x-15-\left(-15\right)=-3\sqrt{5}-\left(-15\right)$$

Subtracting -15 from itself leaves 0.

$$x=3\sqrt{5}-\left(-15\right) x=-3\sqrt{5}-\left(-15\right)$$

Subtract -15 from 3\sqrt{5}.

$$x=3\sqrt{5}+15$$

Subtract -15 from -3\sqrt{5}.

$$x=15-3\sqrt{5}$$

The equation is now solved.

$$x=3\sqrt{5}+15 x=15-3\sqrt{5}$$