Solve (2x-3)^2=29

$$( 2 x - 3 ) ^ { 2 } = 29$$

Solve for x

$$x = \frac{\sqrt{29} + 3}{2} \approx 4.192582404$$

$$x=\frac{3-\sqrt{29}}{2}\approx -1.192582404$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2x-3=\sqrt{29} 2x-3=-\sqrt{29}$$

Add 3 to both sides of the equation.

$$2x-3-\left(-3\right)=\sqrt{29}-\left(-3\right) 2x-3-\left(-3\right)=-\sqrt{29}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$2x=\sqrt{29}-\left(-3\right) 2x=-\sqrt{29}-\left(-3\right)$$

Subtract -3 from \sqrt{29}.

$$2x=\sqrt{29}+3$$

Subtract -3 from -\sqrt{29}.

$$2x=3-\sqrt{29}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{29}+3}{2} \frac{2x}{2}=\frac{3-\sqrt{29}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{29}+3}{2} x=\frac{3-\sqrt{29}}{2}$$