Solve 2(y-2/2)=(x-4/2)^2

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

Solve for y

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

Steps for Solving Linear Equation

Divide 2 by 2 to get 1.

$$2\left(y-1\right)=\left(x-\frac{4}{2}\right)^{2}$$

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

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

Divide 4 by 2 to get 2.

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

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

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

Add 2 to both sides.

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

Add 4 and 2 to get 6.

$$2y=x^{2}-4x+6$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{x^{2}-4x+6}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{x^{2}-4x+6}{2}$$

Divide x^{2}-4x+6 by 2.

$$y=\frac{x^{2}}{2}-2x+3$$

Solve for x (complex solution)

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

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

Solve for x

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

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