Solve y=(x-100)^2-2

$$y = ( x - 100 ) ^ { 2 } - 2$$

Solve for y

$$y=\left(x-100\right)^{2}-2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-100\right)^{2}.

$$y=x^{2}-200x+10000-2$$

Subtract 2 from 10000 to get 9998.

$$y=x^{2}-200x+9998$$

Solve for x (complex solution)

$$x=-\sqrt{y+2}+100$$

$$x=\sqrt{y+2}+100$$

Solve for x

$$x=-\sqrt{y+2}+100$$

$$x=\sqrt{y+2}+100\text{, }y\geq -2$$