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

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

Solve for y

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

Solution Steps

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

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

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

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

Combine -2x and 2x to get 0.

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

Subtract 2 from 1 to get -1.

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

Add -1 and 3 to get 2.

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

Solve for x (complex solution)

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

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

Solve for x

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

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