Solve x=frac{sqrt{2left(y-1right)}}{2}

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

Solve for y

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

$$x\geq 0$$

Steps for Solving Radical Equations

Use the distributive property to multiply 2 by y-1.

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

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

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

Multiply both sides by 2.

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

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

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

Divide x by \frac{1}{2} by multiplying x by the reciprocal of \frac{1}{2}.

$$\sqrt{2y-2}=2x$$

Square both sides of the equation.

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

Add 2 to both sides of the equation.

$$2y-2-\left(-2\right)=4x^{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$2y=4x^{2}-\left(-2\right)$$

Subtract -2 from 4x^{2}.

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

Divide both sides by 2.

$$\frac{2y}{2}=\frac{4x^{2}+2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{4x^{2}+2}{2}$$

Divide 4x^{2}+2 by 2.

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

Solve for y (complex solution)

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

$$arg(x)<\pi \text{ or }x=0$$

Solve for x

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

$$y\geq 1$$