Solve y=30x-5left(x+1right)^2

$$y = 30x-5 { \left( x+1 \right) }^{ 2 }$$

Solve for y

$$y=-5\left(x+1\right)^{2}+30x$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$y=30x-5\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -5 by x^{2}+2x+1.

$$y=30x-5x^{2}-10x-5$$

Combine 30x and -10x to get 20x.

$$y=20x-5x^{2}-5$$

Solve for x (complex solution)

$$x=\frac{\sqrt{75-5y}}{5}+2$$

$$x=-\frac{\sqrt{75-5y}}{5}+2$$

Solve for x

$$x=\frac{\sqrt{75-5y}}{5}+2$$

$$x=-\frac{\sqrt{75-5y}}{5}+2\text{, }y\leq 15$$