Solve (1/2*(10-x)(3/2x))+(1/2(10)(10-3/2x))

$$( \frac{ 1 }{ 2 } \times (10-x)( \frac{ 3 }{ 2 } x))+( \frac{ 1 }{ 2 } (10)(10- \frac{ 3 }{ 2 } x))$$

Evaluate

$$-\frac{3x^{2}}{4}+50$$

Solution Steps

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 2}\left(10-x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$\frac{3}{4}\left(10-x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply \frac{3}{4} by 10-x.

$$\left(\frac{3}{4}\times 10+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Express \frac{3}{4}\times 10 as a single fraction.

$$\left(\frac{3\times 10}{4}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply 3 and 10 to get 30.

$$\left(\frac{30}{4}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{15}{2}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$\left(\frac{15}{2}-\frac{3}{4}x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply \frac{15}{2}-\frac{3}{4}x by x.

$$\frac{15}{2}x-\frac{3}{4}xx+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

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

$$\frac{15}{2}x-\frac{3}{4}x^{2}+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+\frac{10}{2}\left(10-\frac{3}{2}x\right)$$

Divide 10 by 2 to get 5.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+5\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply 5 by 10-\frac{3}{2}x.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+5\left(-\frac{3}{2}\right)x$$

Express 5\left(-\frac{3}{2}\right) as a single fraction.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+\frac{5\left(-3\right)}{2}x$$

Multiply 5 and -3 to get -15.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+\frac{-15}{2}x$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50-\frac{15}{2}x$$

Combine \frac{15}{2}x and -\frac{15}{2}x to get 0.

$$-\frac{3}{4}x^{2}+50$$

Expand

$$-\frac{3x^{2}}{4}+50$$

Solution Steps

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 2}\left(10-x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$\frac{3}{4}\left(10-x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply \frac{3}{4} by 10-x.

$$\left(\frac{3}{4}\times 10+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Express \frac{3}{4}\times 10 as a single fraction.

$$\left(\frac{3\times 10}{4}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply 3 and 10 to get 30.

$$\left(\frac{30}{4}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{15}{2}+\frac{3}{4}\left(-1\right)x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$\left(\frac{15}{2}-\frac{3}{4}x\right)x+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply \frac{15}{2}-\frac{3}{4}x by x.

$$\frac{15}{2}x-\frac{3}{4}xx+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

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

$$\frac{15}{2}x-\frac{3}{4}x^{2}+\frac{1}{2}\times 10\left(10-\frac{3}{2}x\right)$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+\frac{10}{2}\left(10-\frac{3}{2}x\right)$$

Divide 10 by 2 to get 5.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+5\left(10-\frac{3}{2}x\right)$$

Use the distributive property to multiply 5 by 10-\frac{3}{2}x.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+5\left(-\frac{3}{2}\right)x$$

Express 5\left(-\frac{3}{2}\right) as a single fraction.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+\frac{5\left(-3\right)}{2}x$$

Multiply 5 and -3 to get -15.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50+\frac{-15}{2}x$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{15}{2}x-\frac{3}{4}x^{2}+50-\frac{15}{2}x$$

Combine \frac{15}{2}x and -\frac{15}{2}x to get 0.

$$-\frac{3}{4}x^{2}+50$$