Solve -c(x)=200+50/x+x^2/5

$$- c ( x ) = 200 + \frac { 50 } { x } + \frac { x ^ { 2 } } { 5 }$$

Solve for c

$$c=-\frac{x^{3}+1000x+250}{5x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$\left(-c\right)x\times 5x=5x\times 200+5\times 50+xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-c\right)x\times 5x=5x\times 200+5\times 50+x^{3}$$

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

$$\left(-c\right)x^{2}\times 5=5x\times 200+5\times 50+x^{3}$$

Multiply 5 and 200 to get 1000.

$$\left(-c\right)x^{2}\times 5=1000x+5\times 50+x^{3}$$

Multiply 5 and 50 to get 250.

$$\left(-c\right)x^{2}\times 5=1000x+250+x^{3}$$

Multiply -1 and 5 to get -5.

$$-5cx^{2}=1000x+250+x^{3}$$

The equation is in standard form.

$$\left(-5x^{2}\right)c=x^{3}+1000x+250$$

Divide both sides by -5x^{2}.

$$\frac{\left(-5x^{2}\right)c}{-5x^{2}}=\frac{x^{3}+1000x+250}{-5x^{2}}$$

Dividing by -5x^{2} undoes the multiplication by -5x^{2}.

$$c=\frac{x^{3}+1000x+250}{-5x^{2}}$$

Divide 1000x+250+x^{3} by -5x^{2}.

$$c=-\frac{x}{5}-\frac{200x+50}{x^{2}}$$