Solve (3x-1)^2-9=-2

$$( 3 x - 1 ) ^ { 2 } - 9 = - 2$$

Solve for x

$$x = \frac{\sqrt{7} + 1}{3} \approx 1.215250437$$

$$x=\frac{1-\sqrt{7}}{3}\approx -0.54858377$$

Steps by Finding Square Root

Add 9 to both sides of the equation.

$$\left(3x-1\right)^{2}-9+9=-2+9$$

Subtracting 9 from itself leaves 0.

$$\left(3x-1\right)^{2}=-2+9$$

Add -2 to 9.

$$\left(3x-1\right)^{2}=7$$

Take the square root of both sides of the equation.

$$3x-1=\sqrt{7} 3x-1=-\sqrt{7}$$

Add 1 to both sides of the equation.

$$3x-1-\left(-1\right)=\sqrt{7}-\left(-1\right) 3x-1-\left(-1\right)=-\sqrt{7}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$3x=\sqrt{7}-\left(-1\right) 3x=-\sqrt{7}-\left(-1\right)$$

Subtract -1 from \sqrt{7}.

$$3x=\sqrt{7}+1$$

Subtract -1 from -\sqrt{7}.

$$3x=1-\sqrt{7}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\sqrt{7}+1}{3} \frac{3x}{3}=\frac{1-\sqrt{7}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\sqrt{7}+1}{3} x=\frac{1-\sqrt{7}}{3}$$