Solve 3/x^2=57

$$\frac { 3 } { x ^ { 2 } } = 57$$

Solve for x

$$x=\frac{\sqrt{19}}{19}\approx 0.229415734$$

$$x=-\frac{\sqrt{19}}{19}\approx -0.229415734$$

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 x^{2}.

$$3=57x^{2}$$

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

$$57x^{2}=3$$

Divide both sides by 57.

$$x^{2}=\frac{3}{57}$$

Reduce the fraction \frac{3}{57} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{1}{19}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{19}}{19} x=-\frac{\sqrt{19}}{19}$$

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 x^{2}.

$$3=57x^{2}$$

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

$$57x^{2}=3$$

Subtract 3 from both sides.

$$57x^{2}-3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 57 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 57\left(-3\right)}}{2\times 57}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 57\left(-3\right)}}{2\times 57}$$

Multiply -4 times 57.

$$x=\frac{0±\sqrt{-228\left(-3\right)}}{2\times 57}$$

Multiply -228 times -3.

$$x=\frac{0±\sqrt{684}}{2\times 57}$$

Take the square root of 684.

$$x=\frac{0±6\sqrt{19}}{2\times 57}$$

Multiply 2 times 57.

$$x=\frac{0±6\sqrt{19}}{114}$$

Now solve the equation x=\frac{0±6\sqrt{19}}{114} when ± is plus.

$$x=\frac{\sqrt{19}}{19}$$

Now solve the equation x=\frac{0±6\sqrt{19}}{114} when ± is minus.

$$x=-\frac{\sqrt{19}}{19}$$

The equation is now solved.

$$x=\frac{\sqrt{19}}{19} x=-\frac{\sqrt{19}}{19}$$