Solve x=2(1-y)^2

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

Solve for x

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-y\right)^{2}.

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

Use the distributive property to multiply 2 by 1-2y+y^{2}.

$$x=2-4y+2y^{2}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{2x}}{2}+1$$

$$y=-\frac{\sqrt{2x}}{2}+1$$

Solve for y

$$y=\frac{\sqrt{2x}}{2}+1$$

$$y=-\frac{\sqrt{2x}}{2}+1\text{, }x\geq 0$$