Solve y=0.050left(x-100right)^2

$$y=0.050 { \left(x-100 \right) }^{ 2 }$$

Solve for y

$$y=\frac{\left(x-100\right)^{2}}{20}$$

Solution Steps

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

$$y=0.05\left(x^{2}-200x+10000\right)$$

Use the distributive property to multiply 0.05 by x^{2}-200x+10000.

$$y=0.05x^{2}-10x+500$$

Solve for x (complex solution)

$$x=-2\sqrt{5y}+100$$

$$x=2\sqrt{5y}+100$$

Solve for x

$$x=-2\sqrt{5y}+100$$

$$x=2\sqrt{5y}+100\text{, }y\geq 0$$