Solve f=x^2+(20-4x)^2

$$f = x ^ { 2 } + ( 20 - 4 x ) ^ { 2 }$$

Solve for f

$$f=17x^{2}-160x+400$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20-4x\right)^{2}.

$$f=x^{2}+400-160x+16x^{2}$$

Combine x^{2} and 16x^{2} to get 17x^{2}.

$$f=17x^{2}+400-160x$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{17f-400}+80}{17}$$

$$x=\frac{\sqrt{17f-400}+80}{17}$$

Solve for x

$$x=\frac{-\sqrt{17f-400}+80}{17}$$

$$x=\frac{\sqrt{17f-400}+80}{17}\text{, }f\geq \frac{400}{17}$$