Solve w=(x-100)(80+130-x/5)

$$w = ( x - 100 ) ( 80 + \frac { 130 - x } { 5 } )$$

Solve for w

$$w=-\frac{\left(x-530\right)\left(x-100\right)}{5}$$

Solution Steps

Use the distributive property to multiply x-100 by 80+\frac{130-x}{5}.

$$w=80x+x\times \frac{130-x}{5}-8000-100\times \frac{130-x}{5}$$

Express x\times \frac{130-x}{5} as a single fraction.

$$w=80x+\frac{x\left(130-x\right)}{5}-8000-100\times \frac{130-x}{5}$$

Cancel out 5, the greatest common factor in 100 and 5.

$$w=80x+\frac{x\left(130-x\right)}{5}-8000-20\left(130-x\right)$$

Use the distributive property to multiply -20 by 130-x.

$$w=80x+\frac{x\left(130-x\right)}{5}-8000-2600+20x$$

Subtract 2600 from -8000 to get -10600.

$$w=80x+\frac{x\left(130-x\right)}{5}-10600+20x$$

Combine 80x and 20x to get 100x.

$$w=100x+\frac{x\left(130-x\right)}{5}-10600$$

Use the distributive property to multiply x by 130-x.

$$w=100x+\frac{130x-x^{2}}{5}-10600$$

Divide each term of 130x-x^{2} by 5 to get 26x-\frac{1}{5}x^{2}.

$$w=100x+26x-\frac{1}{5}x^{2}-10600$$

Combine 100x and 26x to get 126x.

$$w=126x-\frac{1}{5}x^{2}-10600$$

Solve for x (complex solution)

$$x=\sqrt{46225-5w}+315$$

$$x=-\sqrt{46225-5w}+315$$

Solve for x

$$x=\sqrt{46225-5w}+315$$

$$x=-\sqrt{46225-5w}+315\text{, }w\leq 9245$$