Solve z=y^2+x-1

$$z = y ^ { 2 } + x - 1$$

Solve for x

$$x=1+z-y^{2}$$

Solution Steps

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

$$y^{2}+x-1=z$$

Subtract y^{2} from both sides.

$$x-1=z-y^{2}$$

Add 1 to both sides.

$$x=z-y^{2}+1$$

Solve for y (complex solution)

$$y=-\sqrt{1+z-x}$$

$$y=\sqrt{1+z-x}$$

Solve for y

$$y=\sqrt{1+z-x}$$

$$y=-\sqrt{1+z-x}\text{, }z\geq -\left(1-x\right)$$