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

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

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-1\right)^{2}.

$$9x^{2}-6x+1=9x^{2}-1$$

Subtract 9x^{2} from both sides.

$$9x^{2}-6x+1-9x^{2}=-1$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-6x+1=-1$$

Subtract 1 from both sides.

$$-6x=-1-1$$

Subtract 1 from -1 to get -2.

$$-6x=-2$$

Divide both sides by -6.

$$x=\frac{-2}{-6}$$

Reduce the fraction \frac{-2}{-6} to lowest terms by extracting and canceling out -2.

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