Solve xP=80x-0.1x^2-500+20x

$$xP = 80x-0.1 { x }^{ 2 } -500+20x$$

Solve for P

$$P=-\frac{x}{10}+100-\frac{500}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Combine 80x and 20x to get 100x.

$$xP=100x-0.1x^{2}-500$$

The equation is in standard form.

$$xP=-\frac{x^{2}}{10}+100x-500$$

Divide both sides by x.

$$\frac{xP}{x}=\frac{-\frac{x^{2}}{10}+100x-500}{x}$$

Dividing by x undoes the multiplication by x.

$$P=\frac{-\frac{x^{2}}{10}+100x-500}{x}$$

Divide 100x-\frac{x^{2}}{10}-500 by x.

$$P=-\frac{x}{10}+100-\frac{500}{x}$$

Solve for x (complex solution)

$$x=5\sqrt{P^{2}-200P+9800}-5P+500$$

$$x=-5\sqrt{P^{2}-200P+9800}-5P+500$$

Solve for x

$$x=5\sqrt{P^{2}-200P+9800}-5P+500$$

$$x=-5\sqrt{P^{2}-200P+9800}-5P+500\text{, }P\geq 10\sqrt{2}+100\text{ or }P\leq 100-10\sqrt{2}$$