Solve (2x-1)^2=7

$$( 2 x - 1 ) ^ { 2 } = 7$$

Solve for x

$$x = \frac{\sqrt{7} + 1}{2} \approx 1.822875656$$

$$x=\frac{1-\sqrt{7}}{2}\approx -0.822875656$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$2x-1=\sqrt{7} 2x-1=-\sqrt{7}$$

Add 1 to both sides of the equation.

$$2x-1-\left(-1\right)=\sqrt{7}-\left(-1\right) 2x-1-\left(-1\right)=-\sqrt{7}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$2x=\sqrt{7}-\left(-1\right) 2x=-\sqrt{7}-\left(-1\right)$$

Subtract -1 from \sqrt{7}.

$$2x=\sqrt{7}+1$$

Subtract -1 from -\sqrt{7}.

$$2x=1-\sqrt{7}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{7}+1}{2} \frac{2x}{2}=\frac{1-\sqrt{7}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{7}+1}{2} x=\frac{1-\sqrt{7}}{2}$$