Solve 2x^2=1-a

$$2 x ^ { 2 } = 1 - a$$

Solve for a

$$a=1-2x^{2}$$

Steps for Solving Linear Equation

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

$$1-a=2x^{2}$$

Subtract 1 from both sides.

$$-a=2x^{2}-1$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 2x^{2}-1 by -1.

$$a=1-2x^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2-2a}}{2}$$

$$x=\frac{\sqrt{2-2a}}{2}$$

Solve for x

$$x=\frac{\sqrt{2-2a}}{2}$$

$$x=-\frac{\sqrt{2-2a}}{2}\text{, }a\leq 1$$