Solve x^2=1/169

$$x ^ { 2 } = \frac { 1 } { 169 }$$

Solve for x

$$x=\frac{1}{13}\approx 0.076923077$$

$$x=-\frac{1}{13}\approx -0.076923077$$

Steps Using Difference of Squares

Subtract \frac{1}{169} from both sides.

$$x^{2}-\frac{1}{169}=0$$

Multiply both sides by 169.

$$169x^{2}-1=0$$

Consider 169x^{2}-1. Rewrite 169x^{2}-1 as \left(13x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(13x-1\right)\left(13x+1\right)=0$$

To find equation solutions, solve 13x-1=0 and 13x+1=0.

$$x=\frac{1}{13} x=-\frac{1}{13}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{1}{13} x=-\frac{1}{13}$$

Steps Using the Quadratic Formula

Subtract \frac{1}{169} from both sides.

$$x^{2}-\frac{1}{169}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{169} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{169}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{169}\right)}}{2}$$

Multiply -4 times -\frac{1}{169}.

$$x=\frac{0±\sqrt{\frac{4}{169}}}{2}$$

Take the square root of \frac{4}{169}.

$$x=\frac{0±\frac{2}{13}}{2}$$

Now solve the equation x=\frac{0±\frac{2}{13}}{2} when ± is plus.

$$x=\frac{1}{13}$$

Now solve the equation x=\frac{0±\frac{2}{13}}{2} when ± is minus.

$$x=-\frac{1}{13}$$

The equation is now solved.

$$x=\frac{1}{13} x=-\frac{1}{13}$$