Solve y=(x^2+(10-x)^2)pi

$$y = ( x ^ { 2 } + ( 10 - x ) ^ { 2 } ) \pi$$

Solve for y

$$y=2\pi \left(x^{2}-10x+50\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-x\right)^{2}.

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

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

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

Use the distributive property to multiply 2x^{2}+100-20x by \pi .

$$y=2x^{2}\pi +100\pi -20x\pi$$

Solve for x

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

$$x=-\frac{\sqrt{\frac{2y}{\pi }-100}}{2}+5\text{, }y\geq 50\pi$$