Solve 5=-m^2+2/2

$$5 = \frac { - m ^ { 2 } + 2 } { 2 }$$

Solve for m

$$m=-2\sqrt{2}i\approx -0-2.828427125i$$

$$m=2\sqrt{2}i\approx 2.828427125i$$

Steps by Finding Square Root

Multiply both sides by 2.

$$5\times 2=-m^{2}+2$$

Multiply 5 and 2 to get 10.

$$10=-m^{2}+2$$

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

$$-m^{2}+2=10$$

Subtract 2 from both sides.

$$-m^{2}=10-2$$

Subtract 2 from 10 to get 8.

$$-m^{2}=8$$

Divide both sides by -1.

$$m^{2}=-8$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$5\times 2=-m^{2}+2$$

Multiply 5 and 2 to get 10.

$$10=-m^{2}+2$$

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

$$-m^{2}+2=10$$

Subtract 10 from both sides.

$$-m^{2}+2-10=0$$

Subtract 10 from 2 to get -8.

$$-m^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$m=\frac{0±\sqrt{4\left(-8\right)}}{2\left(-1\right)}$$

Multiply 4 times -8.

$$m=\frac{0±\sqrt{-32}}{2\left(-1\right)}$$

Take the square root of -32.

$$m=\frac{0±4\sqrt{2}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$m=\frac{0±4\sqrt{2}i}{-2}$$

Now solve the equation m=\frac{0±4\sqrt{2}i}{-2} when ± is plus.

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

Now solve the equation m=\frac{0±4\sqrt{2}i}{-2} when ± is minus.

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

The equation is now solved.

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