Solve 197=73.8/h^2

$$197 = \frac { 73.8 } { h ^ { 2 } }$$

Solve for h

$$h=\frac{3\sqrt{40385}}{985}\approx 0.612061508$$

$$h=-\frac{3\sqrt{40385}}{985}\approx -0.612061508$$

Steps by Finding Square Root

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by h^{2}.

$$197h^{2}=73.8$$

Divide both sides by 197.

$$h^{2}=\frac{73.8}{197}$$

Expand \frac{73.8}{197} by multiplying both numerator and the denominator by 10.

$$h^{2}=\frac{738}{1970}$$

Reduce the fraction \frac{738}{1970} to lowest terms by extracting and canceling out 2.

$$h^{2}=\frac{369}{985}$$

Take the square root of both sides of the equation.

$$h=\frac{3\sqrt{40385}}{985} h=-\frac{3\sqrt{40385}}{985}$$

Steps Using the Quadratic Formula

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by h^{2}.

$$197h^{2}=73.8$$

Subtract 73.8 from both sides.

$$197h^{2}-73.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 197 for a, 0 for b, and -73.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 197\left(-73.8\right)}}{2\times 197}$$

Square 0.

$$h=\frac{0±\sqrt{-4\times 197\left(-73.8\right)}}{2\times 197}$$

Multiply -4 times 197.

$$h=\frac{0±\sqrt{-788\left(-73.8\right)}}{2\times 197}$$

Multiply -788 times -73.8.

$$h=\frac{0±\sqrt{58154.4}}{2\times 197}$$

Take the square root of 58154.4.

$$h=\frac{0±\frac{6\sqrt{40385}}{5}}{2\times 197}$$

Multiply 2 times 197.

$$h=\frac{0±\frac{6\sqrt{40385}}{5}}{394}$$

Now solve the equation h=\frac{0±\frac{6\sqrt{40385}}{5}}{394} when ± is plus.

$$h=\frac{3\sqrt{40385}}{985}$$

Now solve the equation h=\frac{0±\frac{6\sqrt{40385}}{5}}{394} when ± is minus.

$$h=-\frac{3\sqrt{40385}}{985}$$

The equation is now solved.

$$h=\frac{3\sqrt{40385}}{985} h=-\frac{3\sqrt{40385}}{985}$$