Solve x^2+y^2=(x-1)^2+3

$$x ^ { 2 } + y ^ { 2 } = ( x - 1 ) ^ { 2 } + 3$$

Solve for x

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

Steps for Solving Linear Equation

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

$$x^{2}+y^{2}=x^{2}-2x+1+3$$

Add 1 and 3 to get 4.

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

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

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

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

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

Subtract 4 from both sides.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

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

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

Solve for y (complex solution)

$$y=-\sqrt{4-2x}$$

$$y=\sqrt{4-2x}$$

Solve for y

$$y=\sqrt{4-2x}$$

$$y=-\sqrt{4-2x}\text{, }x\leq 2$$