Solve y=left(1200-240xright)^2+80x*80x

$$y= { \left(1200-240x \right) }^{ 2 } +80x \times 80x$$

Solve for y

$$y=64000x^{2}-576000x+1440000$$

Solution Steps

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

$$y=\left(1200-240x\right)^{2}+80x^{2}\times 80$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1200-240x\right)^{2}.

$$y=1440000-576000x+57600x^{2}+80x^{2}\times 80$$

Multiply 80 and 80 to get 6400.

$$y=1440000-576000x+57600x^{2}+6400x^{2}$$

Combine 57600x^{2} and 6400x^{2} to get 64000x^{2}.

$$y=1440000-576000x+64000x^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10y-1440000}}{800}+\frac{9}{2}$$

$$x=\frac{\sqrt{10y-1440000}}{800}+\frac{9}{2}$$

Solve for x

$$x=-\frac{\sqrt{10y-1440000}}{800}+\frac{9}{2}$$

$$x=\frac{\sqrt{10y-1440000}}{800}+\frac{9}{2}\text{, }y\geq 144000$$