Solve (5x-1)^2=1/9

$$( 5 x - 1 ) ^ { 2 } = \frac { 1 } { 9 }$$

Solve for x

$$x=\frac{4}{15}\approx 0.266666667$$

$$x=\frac{2}{15}\approx 0.133333333$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Add 1 to both sides of the equation.

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

Subtracting -1 from itself leaves 0.

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

Subtract -1 from \frac{1}{3}.

$$5x=\frac{4}{3}$$

Subtract -1 from -\frac{1}{3}.

$$5x=\frac{2}{3}$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{\frac{4}{3}}{5} \frac{5x}{5}=\frac{\frac{2}{3}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{\frac{4}{3}}{5} x=\frac{\frac{2}{3}}{5}$$

Divide \frac{4}{3} by 5.

$$x=\frac{4}{15}$$

Divide \frac{2}{3} by 5.

$$x=\frac{2}{15}$$

The equation is now solved.

$$x=\frac{4}{15} x=\frac{2}{15}$$