Solve 1/5x^2=14

$$\frac{ 1 }{ 5 } { x }^{ 2 } =14$$

Solve for x

$$x=\sqrt{70}\approx 8.366600265$$

$$x=-\sqrt{70}\approx -8.366600265$$

Steps by Finding Square Root

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x^{2}=14\times 5$$

Multiply 14 and 5 to get 70.

$$x^{2}=70$$

Take the square root of both sides of the equation.

$$x=\sqrt{70} x=-\sqrt{70}$$

Steps Using the Quadratic Formula

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x^{2}=14\times 5$$

Multiply 14 and 5 to get 70.

$$x^{2}=70$$

Subtract 70 from both sides.

$$x^{2}-70=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -70 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-70\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-70\right)}}{2}$$

Multiply -4 times -70.

$$x=\frac{0±\sqrt{280}}{2}$$

Take the square root of 280.

$$x=\frac{0±2\sqrt{70}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{2} when ± is plus.

$$x=\sqrt{70}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{2} when ± is minus.

$$x=-\sqrt{70}$$

The equation is now solved.

$$x=\sqrt{70} x=-\sqrt{70}$$