Solve (x-2)^2+4=9

$$( x - 2 ) ^ { 2 } + 4 = 9$$

Solve for x

$$x=\sqrt{5}+2\approx 4.236067977$$

$$x=2-\sqrt{5}\approx -0.236067977$$

Steps by Finding Square Root

Subtract 4 from both sides of the equation.

$$\left(x-2\right)^{2}+4-4=9-4$$

Subtracting 4 from itself leaves 0.

$$\left(x-2\right)^{2}=9-4$$

Subtract 4 from 9.

$$\left(x-2\right)^{2}=5$$

Take the square root of both sides of the equation.

$$x-2=\sqrt{5} x-2=-\sqrt{5}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\sqrt{5}-\left(-2\right) x-2-\left(-2\right)=-\sqrt{5}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\sqrt{5}-\left(-2\right) x=-\sqrt{5}-\left(-2\right)$$

Subtract -2 from \sqrt{5}.

$$x=\sqrt{5}+2$$

Subtract -2 from -\sqrt{5}.

$$x=2-\sqrt{5}$$

The equation is now solved.

$$x=\sqrt{5}+2 x=2-\sqrt{5}$$