Solve 4m^2+6=-154

$$4 m ^ { 2 } + 6 = - 154$$

Solve for m

$$m=-2\sqrt{10}i\approx -0-6.32455532i$$

$$m=2\sqrt{10}i\approx 6.32455532i$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$4m^{2}=-154-6$$

Subtract 6 from -154 to get -160.

$$4m^{2}=-160$$

Divide both sides by 4.

$$m^{2}=\frac{-160}{4}$$

Divide -160 by 4 to get -40.

$$m^{2}=-40$$

The equation is now solved.

$$m=2\sqrt{10}i m=-2\sqrt{10}i$$

Steps Using the Quadratic Formula

Add 154 to both sides.

$$4m^{2}+6+154=0$$

Add 6 and 154 to get 160.

$$4m^{2}+160=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 160 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 4\times 160}}{2\times 4}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 4\times 160}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{0±\sqrt{-16\times 160}}{2\times 4}$$

Multiply -16 times 160.

$$m=\frac{0±\sqrt{-2560}}{2\times 4}$$

Take the square root of -2560.

$$m=\frac{0±16\sqrt{10}i}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{0±16\sqrt{10}i}{8}$$

Now solve the equation m=\frac{0±16\sqrt{10}i}{8} when ± is plus.

$$m=2\sqrt{10}i$$

Now solve the equation m=\frac{0±16\sqrt{10}i}{8} when ± is minus.

$$m=-2\sqrt{10}i$$

The equation is now solved.

$$m=2\sqrt{10}i m=-2\sqrt{10}i$$