Solve y=x(-2x+100)-18(-2x+100)

$$y = x ( - 2 x + 100 ) - 18 ( - 2 x + 100 )$$

Solve for y

$$y=2\left(50-x\right)\left(x-18\right)$$

Solution Steps

Use the distributive property to multiply x by -2x+100.

$$y=-2x^{2}+100x-18\left(-2x+100\right)$$

Use the distributive property to multiply -18 by -2x+100.

$$y=-2x^{2}+100x+36x-1800$$

Combine 100x and 36x to get 136x.

$$y=-2x^{2}+136x-1800$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1024-2y}}{2}+34$$

$$x=-\frac{\sqrt{1024-2y}}{2}+34$$

Solve for x

$$x=\frac{\sqrt{1024-2y}}{2}+34$$

$$x=-\frac{\sqrt{1024-2y}}{2}+34\text{, }y\leq 512$$