Solve (2x-3)^2-5=0

$$( 2 x - 3 ) ^ { 2 } - 5 = 0$$

Solve for x

$$x = \frac{\sqrt{5} + 3}{2} \approx 2.618033989$$

$$x=\frac{3-\sqrt{5}}{2}\approx 0.381966011$$

Steps by Finding Square Root

Add 5 to both sides of the equation.

$$\left(2x-3\right)^{2}-5+5=5$$

Subtracting 5 from itself leaves 0.

$$\left(2x-3\right)^{2}=5$$

Take the square root of both sides of the equation.

$$2x-3=\sqrt{5} 2x-3=-\sqrt{5}$$

Add 3 to both sides of the equation.

$$2x-3-\left(-3\right)=\sqrt{5}-\left(-3\right) 2x-3-\left(-3\right)=-\sqrt{5}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$2x=\sqrt{5}-\left(-3\right) 2x=-\sqrt{5}-\left(-3\right)$$

Subtract -3 from \sqrt{5}.

$$2x=\sqrt{5}+3$$

Subtract -3 from -\sqrt{5}.

$$2x=3-\sqrt{5}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{5}+3}{2} \frac{2x}{2}=\frac{3-\sqrt{5}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{5}+3}{2} x=\frac{3-\sqrt{5}}{2}$$