Solve =1quad[(3*-1/2)-2]x^2-2[(5x-1/2)-2]x

$$= 1 \quad [ ( 3 \cdot - \frac { 1 } { 2 } ) - 2 ] x ^ { 2 } - 2 [ ( 5 x - \frac { 1 } { 2 } ) - 2 ] x$$

Evaluate

$$\frac{x\left(10-27x\right)}{2}$$

Solution Steps

Multiply 3 and -\frac{1}{2} to get -\frac{3}{2}.

$$1\left(-\frac{3}{2}-2\right)x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Subtract 2 from -\frac{3}{2} to get -\frac{7}{2}.

$$1\left(-\frac{7}{2}\right)x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Multiply 1 and -\frac{7}{2} to get -\frac{7}{2}.

$$-\frac{7}{2}x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Subtract 2 from -\frac{1}{2} to get -\frac{5}{2}.

$$-\frac{7}{2}x^{2}-2\left(5x-\frac{5}{2}\right)x$$

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

$$-\frac{7}{2}x^{2}+\left(-10x+5\right)x$$

Use the distributive property to multiply -10x+5 by x.

$$-\frac{7}{2}x^{2}-10x^{2}+5x$$

Combine -\frac{7}{2}x^{2} and -10x^{2} to get -\frac{27}{2}x^{2}.

$$-\frac{27}{2}x^{2}+5x$$

Expand

$$-\frac{27x^{2}}{2}+5x$$

Solution Steps

Multiply 3 and -\frac{1}{2} to get -\frac{3}{2}.

$$1\left(-\frac{3}{2}-2\right)x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Subtract 2 from -\frac{3}{2} to get -\frac{7}{2}.

$$1\left(-\frac{7}{2}\right)x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Multiply 1 and -\frac{7}{2} to get -\frac{7}{2}.

$$-\frac{7}{2}x^{2}-2\left(5x-\frac{1}{2}-2\right)x$$

Subtract 2 from -\frac{1}{2} to get -\frac{5}{2}.

$$-\frac{7}{2}x^{2}-2\left(5x-\frac{5}{2}\right)x$$

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

$$-\frac{7}{2}x^{2}+\left(-10x+5\right)x$$

Use the distributive property to multiply -10x+5 by x.

$$-\frac{7}{2}x^{2}-10x^{2}+5x$$

Combine -\frac{7}{2}x^{2} and -10x^{2} to get -\frac{27}{2}x^{2}.

$$-\frac{27}{2}x^{2}+5x$$