Solve (x-100)(-1/2x+190)

$$(x-100)(- \frac{ 1 }{ 2 } x+190)$$

Evaluate

$$\frac{\left(380-x\right)\left(x-100\right)}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x-100 by each term of -\frac{1}{2}x+190.

$$x\left(-\frac{1}{2}\right)x+190x-100\left(-\frac{1}{2}\right)x-19000$$

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

$$x^{2}\left(-\frac{1}{2}\right)+190x-100\left(-\frac{1}{2}\right)x-19000$$

Express -100\left(-\frac{1}{2}\right) as a single fraction.

$$x^{2}\left(-\frac{1}{2}\right)+190x+\frac{-100\left(-1\right)}{2}x-19000$$

Multiply -100 and -1 to get 100.

$$x^{2}\left(-\frac{1}{2}\right)+190x+\frac{100}{2}x-19000$$

Divide 100 by 2 to get 50.

$$x^{2}\left(-\frac{1}{2}\right)+190x+50x-19000$$

Combine 190x and 50x to get 240x.

$$x^{2}\left(-\frac{1}{2}\right)+240x-19000$$

Expand

$$-\frac{x^{2}}{2}+240x-19000$$

Solution Steps

Apply the distributive property by multiplying each term of x-100 by each term of -\frac{1}{2}x+190.

$$x\left(-\frac{1}{2}\right)x+190x-100\left(-\frac{1}{2}\right)x-19000$$

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

$$x^{2}\left(-\frac{1}{2}\right)+190x-100\left(-\frac{1}{2}\right)x-19000$$

Express -100\left(-\frac{1}{2}\right) as a single fraction.

$$x^{2}\left(-\frac{1}{2}\right)+190x+\frac{-100\left(-1\right)}{2}x-19000$$

Multiply -100 and -1 to get 100.

$$x^{2}\left(-\frac{1}{2}\right)+190x+\frac{100}{2}x-19000$$

Divide 100 by 2 to get 50.

$$x^{2}\left(-\frac{1}{2}\right)+190x+50x-19000$$

Combine 190x and 50x to get 240x.

$$x^{2}\left(-\frac{1}{2}\right)+240x-19000$$