Solve (y-2)^2=3-x

$$( y - 2 ) ^ { 2 } = 3 - x$$

Solve for x

$$x=-\left(y-2\right)^{2}+3$$

Steps for Solving Linear Equation

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

$$y^{2}-4y+4=3-x$$

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

$$3-x=y^{2}-4y+4$$

Subtract 3 from both sides.

$$-x=y^{2}-4y+4-3$$

Subtract 3 from 4 to get 1.

$$-x=y^{2}-4y+1$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{y^{2}-4y+1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{y^{2}-4y+1}{-1}$$

Divide y^{2}-4y+1 by -1.

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

Solve for y (complex solution)

$$y=-\sqrt{3-x}+2$$

$$y=\sqrt{3-x}+2$$

Solve for y

$$y=-\sqrt{3-x}+2$$

$$y=\sqrt{3-x}+2\text{, }x\leq 3$$