Solve 70/x^2=18.5

$$\frac{ 70 }{ { x }^{ 2 } } =18.5$$

Solve for x

$$x = \frac{2 \sqrt{1295}}{37} \approx 1.94519505$$

$$x = -\frac{2 \sqrt{1295}}{37} \approx -1.94519505$$

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}.

$$70=18.5x^{2}$$

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

$$18.5x^{2}=70$$

Divide both sides by 18.5.

$$x^{2}=\frac{70}{18.5}$$

Expand \frac{70}{18.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{700}{185}$$

Reduce the fraction \frac{700}{185} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{140}{37}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{1295}}{37} x=-\frac{2\sqrt{1295}}{37}$$

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}.

$$70=18.5x^{2}$$

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

$$18.5x^{2}=70$$

Subtract 70 from both sides.

$$18.5x^{2}-70=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 18.5 for a, 0 for b, and -70 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 18.5\left(-70\right)}}{2\times 18.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 18.5\left(-70\right)}}{2\times 18.5}$$

Multiply -4 times 18.5.

$$x=\frac{0±\sqrt{-74\left(-70\right)}}{2\times 18.5}$$

Multiply -74 times -70.

$$x=\frac{0±\sqrt{5180}}{2\times 18.5}$$

Take the square root of 5180.

$$x=\frac{0±2\sqrt{1295}}{2\times 18.5}$$

Multiply 2 times 18.5.

$$x=\frac{0±2\sqrt{1295}}{37}$$

Now solve the equation x=\frac{0±2\sqrt{1295}}{37} when ± is plus.

$$x=\frac{2\sqrt{1295}}{37}$$

Now solve the equation x=\frac{0±2\sqrt{1295}}{37} when ± is minus.

$$x=-\frac{2\sqrt{1295}}{37}$$

The equation is now solved.

$$x=\frac{2\sqrt{1295}}{37} x=-\frac{2\sqrt{1295}}{37}$$