Solve 4m^2+76=0

$$4 m ^ { 2 } + 76 = 0$$

Solve for m

$$m=-\sqrt{19}i\approx -0-4.358898944i$$

$$m=\sqrt{19}i\approx 4.358898944i$$

Steps by Finding Square Root

Subtract 76 from both sides. Anything subtracted from zero gives its negation.

$$4m^{2}=-76$$

Divide both sides by 4.

$$m^{2}=\frac{-76}{4}$$

Divide -76 by 4 to get -19.

$$m^{2}=-19$$

The equation is now solved.

$$m=\sqrt{19}i m=-\sqrt{19}i$$

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.

$$4m^{2}+76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 4\times 76}}{2\times 4}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 4\times 76}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{0±\sqrt{-16\times 76}}{2\times 4}$$

Multiply -16 times 76.

$$m=\frac{0±\sqrt{-1216}}{2\times 4}$$

Take the square root of -1216.

$$m=\frac{0±8\sqrt{19}i}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{0±8\sqrt{19}i}{8}$$

Now solve the equation m=\frac{0±8\sqrt{19}i}{8} when ± is plus.

$$m=\sqrt{19}i$$

Now solve the equation m=\frac{0±8\sqrt{19}i}{8} when ± is minus.

$$m=-\sqrt{19}i$$

The equation is now solved.

$$m=\sqrt{19}i m=-\sqrt{19}i$$