Solve 2x^2-4+m-1=0

$$2 x ^ { 2 } - 4 + m - 1 = 0$$

Solve for m

$$m=5-2x^{2}$$

Solution Steps

Subtract 1 from -4 to get -5.

$$2x^{2}-5+m=0$$

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

$$-5+m=-2x^{2}$$

Add 5 to both sides.

$$m=-2x^{2}+5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10-2m}}{2}$$

$$x=\frac{\sqrt{10-2m}}{2}$$

Solve for x

$$x=\frac{\sqrt{10-2m}}{2}$$

$$x=-\frac{\sqrt{10-2m}}{2}\text{, }m\leq 5$$