Solve 0=1/2x^2-2-m

$$0 = \frac { 1 } { 2 } x ^ { 2 } - 2 - m$$

Solve for m

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}x^{2}-2-m=0$$

Subtract \frac{1}{2}x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2-m=-\frac{1}{2}x^{2}$$

Add 2 to both sides.

$$-m=-\frac{1}{2}x^{2}+2$$

The equation is in standard form.

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

Divide both sides by -1.

$$\frac{-m}{-1}=\frac{-\frac{x^{2}}{2}+2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$m=\frac{-\frac{x^{2}}{2}+2}{-1}$$

Divide -\frac{x^{2}}{2}+2 by -1.

$$m=\frac{x^{2}}{2}-2$$

Solve for x (complex solution)

$$x=-\sqrt{2\left(m+2\right)}$$

$$x=\sqrt{2\left(m+2\right)}$$

Solve for x

$$x=\sqrt{2\left(m+2\right)}$$

$$x=-\sqrt{2\left(m+2\right)}\text{, }m\geq -2$$