Solve (-1/2x+37)(5x+50)

$$( - \frac { 1 } { 2 } x + 37 ) ( 5 x + 50 )$$

Evaluate

$$\frac{5\left(74-x\right)\left(x+10\right)}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{2}x+37 by each term of 5x+50.

$$-\frac{1}{2}x\times 5x-\frac{1}{2}x\times 50+185x+1850$$

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

$$-\frac{1}{2}x^{2}\times 5-\frac{1}{2}x\times 50+185x+1850$$

Express -\frac{1}{2}\times 5 as a single fraction.

$$\frac{-5}{2}x^{2}-\frac{1}{2}x\times 50+185x+1850$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-\frac{5}{2}x^{2}-\frac{1}{2}x\times 50+185x+1850$$

Express -\frac{1}{2}\times 50 as a single fraction.

$$-\frac{5}{2}x^{2}+\frac{-50}{2}x+185x+1850$$

Divide -50 by 2 to get -25.

$$-\frac{5}{2}x^{2}-25x+185x+1850$$

Combine -25x and 185x to get 160x.

$$-\frac{5}{2}x^{2}+160x+1850$$

Expand

$$-\frac{5x^{2}}{2}+160x+1850$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{2}x+37 by each term of 5x+50.

$$-\frac{1}{2}x\times 5x-\frac{1}{2}x\times 50+185x+1850$$

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

$$-\frac{1}{2}x^{2}\times 5-\frac{1}{2}x\times 50+185x+1850$$

Express -\frac{1}{2}\times 5 as a single fraction.

$$\frac{-5}{2}x^{2}-\frac{1}{2}x\times 50+185x+1850$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-\frac{5}{2}x^{2}-\frac{1}{2}x\times 50+185x+1850$$

Express -\frac{1}{2}\times 50 as a single fraction.

$$-\frac{5}{2}x^{2}+\frac{-50}{2}x+185x+1850$$

Divide -50 by 2 to get -25.

$$-\frac{5}{2}x^{2}-25x+185x+1850$$

Combine -25x and 185x to get 160x.

$$-\frac{5}{2}x^{2}+160x+1850$$