Solve x-(x-3/2)^2

$$x - ( \frac { x - 3 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(1-x\right)\left(x-9\right)}{4}$$

Short Solution Steps

To raise \frac{x-3}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4}{4}.

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

Since \frac{4x}{4} and \frac{\left(x-3\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4x-\left(x-3\right)^{2}.

$$\frac{4x-x^{2}+6x-9}{4}$$

Combine like terms in 4x-x^{2}+6x-9.

$$\frac{10x-x^{2}-9}{4}$$

Expand

$$-\frac{x^{2}}{4}+\frac{5x}{2}-\frac{9}{4}$$

Short Solution Steps

To raise \frac{x-3}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4}{4}.

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

Since \frac{4x}{4} and \frac{\left(x-3\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4x-\left(x-3\right)^{2}.

$$\frac{4x-x^{2}+6x-9}{4}$$

Combine like terms in 4x-x^{2}+6x-9.

$$\frac{10x-x^{2}-9}{4}$$