Solve y=x^2+(26-x)^2

$$y = x ^ { 2 } + ( 26 - x ) ^ { 2 }$$

Solve for y

$$y=2\left(x^{2}-26x+338\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(26-x\right)^{2}.

$$y=x^{2}+676-52x+x^{2}$$

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

$$y=2x^{2}+676-52x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y-676}}{2}+13$$

$$x=\frac{\sqrt{2y-676}}{2}+13$$

Solve for x

$$x=-\frac{\sqrt{2y-676}}{2}+13$$

$$x=\frac{\sqrt{2y-676}}{2}+13\text{, }y\geq 338$$