Solve 1/x^2=1/13

$$\frac{ 1 }{ { x }^{ 2 } } = \frac{ 1 }{ 13 }$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 13x^{2}, the least common multiple of x^{2},13.

$$13=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 13x^{2}, the least common multiple of x^{2},13.

$$13=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=13$$

Subtract 13 from both sides.

$$x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

Multiply -4 times -13.

$$x=\frac{0±\sqrt{52}}{2}$$

Take the square root of 52.

$$x=\frac{0±2\sqrt{13}}{2}$$

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

$$x=\sqrt{13}$$

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

$$x=-\sqrt{13}$$

The equation is now solved.

$$x=\sqrt{13} x=-\sqrt{13}$$