Solve C=x^2-2x-80/x-10-(x-25

$$C = \frac { x ^ { 2 } - 2 x - 80 } { x - 10 } - ( x - 25$$

Solve for C

$$C=33$$

$$x\neq 10$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{x^{2}-2x-80}{x-10}.

$$C=\frac{\left(x-10\right)\left(x+8\right)}{x-10}-\left(x-25\right)$$

Cancel out x-10 in both numerator and denominator.

$$C=x+8-\left(x-25\right)$$

To find the opposite of x-25, find the opposite of each term.

$$C=x+8-x+25$$

Combine x and -x to get 0.

$$C=8+25$$

Add 8 and 25 to get 33.

$$C=33$$

Solve for x

$$x\neq 10$$

$$C=33\text{ and }x\neq 10$$

Steps for Solving Linear Equation

Variable x cannot be equal to 10 since division by zero is not defined. Multiply both sides of the equation by x-10.

$$C\left(x-10\right)=x^{2}-2x-80-\left(x-25\right)\left(x-10\right)$$

Use the distributive property to multiply C by x-10.

$$Cx-10C=x^{2}-2x-80-\left(x-25\right)\left(x-10\right)$$

Use the distributive property to multiply -1 by x-25.

$$Cx-10C=x^{2}-2x-80+\left(-x+25\right)\left(x-10\right)$$

Use the distributive property to multiply -x+25 by x-10 and combine like terms.

$$Cx-10C=x^{2}-2x-80-x^{2}+35x-250$$

Combine x^{2} and -x^{2} to get 0.

$$Cx-10C=-2x-80+35x-250$$

Combine -2x and 35x to get 33x.

$$Cx-10C=33x-80-250$$

Subtract 250 from -80 to get -330.

$$Cx-10C=33x-330$$

Subtract 33x from both sides.

$$Cx-10C-33x=-330$$

Add 10C to both sides.

$$Cx-33x=-330+10C$$

Combine all terms containing x.

$$\left(C-33\right)x=-330+10C$$

The equation is in standard form.

$$\left(C-33\right)x=10C-330$$

Divide both sides by C-33.

$$\frac{\left(C-33\right)x}{C-33}=\frac{10C-330}{C-33}$$

Dividing by C-33 undoes the multiplication by C-33.

$$x=\frac{10C-330}{C-33}$$

Divide -330+10C by C-33.

$$x=10$$

Variable x cannot be equal to 10.

$$x\in \emptyset$$