Solve (x^2-1/2ax)-(2^2+3/2ax-1/4x)-5/4x^2+(2+frac{3}{2}ax)-frac{1}{2}a

$$( x ^ { 2 } - \frac { 1 } { 2 } a x ) - ( 2 ^ { 2 } + \frac { 3 } { 2 } a x - \frac { 1 } { 4 } x ) - \frac { 5 } { 4 } x ^ { 2 } + ( 2 + \frac { 3 } { 2 } a x ) - \frac { 1 } { 2 } a$$

Evaluate

$$\frac{-x^{2}-2ax+x-2a-8}{4}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$x^{2}-\frac{1}{2}ax-\left(4+\frac{3}{2}ax-\frac{1}{4}x\right)-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

To find the opposite of 4+\frac{3}{2}ax-\frac{1}{4}x, find the opposite of each term.

$$x^{2}-\frac{1}{2}ax-4-\frac{3}{2}ax+\frac{1}{4}x-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

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

$$x^{2}-2ax-4+\frac{1}{4}x-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

Combine x^{2} and -\frac{5}{4}x^{2} to get -\frac{1}{4}x^{2}.

$$-\frac{1}{4}x^{2}-2ax-4+\frac{1}{4}x+2+\frac{3}{2}ax-\frac{1}{2}a$$

Add -4 and 2 to get -2.

$$-\frac{1}{4}x^{2}-2ax-2+\frac{1}{4}x+\frac{3}{2}ax-\frac{1}{2}a$$

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

$$-\frac{1}{4}x^{2}-\frac{1}{2}ax-2+\frac{1}{4}x-\frac{1}{2}a$$

Expand

$$-\frac{ax}{2}-\frac{x^{2}}{4}+\frac{x}{4}-\frac{a}{2}-2$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$x^{2}-\frac{1}{2}ax-\left(4+\frac{3}{2}ax-\frac{1}{4}x\right)-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

To find the opposite of 4+\frac{3}{2}ax-\frac{1}{4}x, find the opposite of each term.

$$x^{2}-\frac{1}{2}ax-4-\frac{3}{2}ax+\frac{1}{4}x-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

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

$$x^{2}-2ax-4+\frac{1}{4}x-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{2}a$$

Combine x^{2} and -\frac{5}{4}x^{2} to get -\frac{1}{4}x^{2}.

$$-\frac{1}{4}x^{2}-2ax-4+\frac{1}{4}x+2+\frac{3}{2}ax-\frac{1}{2}a$$

Add -4 and 2 to get -2.

$$-\frac{1}{4}x^{2}-2ax-2+\frac{1}{4}x+\frac{3}{2}ax-\frac{1}{2}a$$

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

$$-\frac{1}{4}x^{2}-\frac{1}{2}ax-2+\frac{1}{4}x-\frac{1}{2}a$$