Solve y=0.10left(x-100right)^2

$$y=0.10 { \left(x-100 \right) }^{ 2 }$$

Solve for y

$$y=\frac{\left(x-100\right)^{2}}{10}$$

Solution Steps

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

$$y=0.1\left(x^{2}-200x+10000\right)$$

Use the distributive property to multiply 0.1 by x^{2}-200x+10000.

$$y=0.1x^{2}-20x+1000$$

Solve for x (complex solution)

$$x=-\sqrt{10y}+100$$

$$x=\sqrt{10y}+100$$

Solve for x

$$x=-\sqrt{10y}+100$$

$$x=\sqrt{10y}+100\text{, }y\geq 0$$