Solve (3x-1)^2=5

$$( 3 x - 1 ) ^ { 2 } = 5$$

Solve for x

$$x = \frac{\sqrt{5} + 1}{3} \approx 1.078689326$$

$$x=\frac{1-\sqrt{5}}{3}\approx -0.412022659$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$3x-1=\sqrt{5} 3x-1=-\sqrt{5}$$

Add 1 to both sides of the equation.

$$3x-1-\left(-1\right)=\sqrt{5}-\left(-1\right) 3x-1-\left(-1\right)=-\sqrt{5}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$3x=\sqrt{5}-\left(-1\right) 3x=-\sqrt{5}-\left(-1\right)$$

Subtract -1 from \sqrt{5}.

$$3x=\sqrt{5}+1$$

Subtract -1 from -\sqrt{5}.

$$3x=1-\sqrt{5}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\sqrt{5}+1}{3} \frac{3x}{3}=\frac{1-\sqrt{5}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\sqrt{5}+1}{3} x=\frac{1-\sqrt{5}}{3}$$