Solve y^2-1/2x=1

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

Solve for x

$$x=2\left(y^{2}-1\right)$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

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

Multiply both sides by -2.

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

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

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

Divide -y^{2}+1 by -\frac{1}{2} by multiplying -y^{2}+1 by the reciprocal of -\frac{1}{2}.

$$x=2y^{2}-2$$

Solve for y (complex solution)

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

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

Solve for y

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

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