Solve 5h^2+375=0

$$5 h ^ { 2 } + 375 = 0$$

Solve for h

$$h=-5\sqrt{3}i\approx -0-8.660254038i$$

$$h=5\sqrt{3}i\approx 8.660254038i$$

Steps by Finding Square Root

Subtract 375 from both sides. Anything subtracted from zero gives its negation.

$$5h^{2}=-375$$

Divide both sides by 5.

$$h^{2}=\frac{-375}{5}$$

Divide -375 by 5 to get -75.

$$h^{2}=-75$$

The equation is now solved.

$$h=5\sqrt{3}i h=-5\sqrt{3}i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5h^{2}+375=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 375 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 5\times 375}}{2\times 5}$$

Square 0.

$$h=\frac{0±\sqrt{-4\times 5\times 375}}{2\times 5}$$

Multiply -4 times 5.

$$h=\frac{0±\sqrt{-20\times 375}}{2\times 5}$$

Multiply -20 times 375.

$$h=\frac{0±\sqrt{-7500}}{2\times 5}$$

Take the square root of -7500.

$$h=\frac{0±50\sqrt{3}i}{2\times 5}$$

Multiply 2 times 5.

$$h=\frac{0±50\sqrt{3}i}{10}$$

Now solve the equation h=\frac{0±50\sqrt{3}i}{10} when ± is plus.

$$h=5\sqrt{3}i$$

Now solve the equation h=\frac{0±50\sqrt{3}i}{10} when ± is minus.

$$h=-5\sqrt{3}i$$

The equation is now solved.

$$h=5\sqrt{3}i h=-5\sqrt{3}i$$