Solve frac{1}2^2-2x1/2-3+(-3)^2

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

Evaluate

$$\frac{25}{4}-x$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Cancel out 2 and 2.

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

Convert 3 to fraction \frac{12}{4}.

$$\frac{1}{4}-x-\frac{12}{4}+\left(-3\right)^{2}$$

Since \frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-12}{4}-x+\left(-3\right)^{2}$$

Subtract 12 from 1 to get -11.

$$-\frac{11}{4}-x+\left(-3\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$-\frac{11}{4}-x+9$$

Convert 9 to fraction \frac{36}{4}.

$$-\frac{11}{4}-x+\frac{36}{4}$$

Since -\frac{11}{4} and \frac{36}{4} have the same denominator, add them by adding their numerators.

$$\frac{-11+36}{4}-x$$

Add -11 and 36 to get 25.

$$\frac{25}{4}-x$$

Factor

$$\frac{25-4x}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{25-4x}{4}$$

Consider 1-4x-12+36. Multiply and combine like terms.

$$-4x+25$$

Rewrite the complete factored expression.

$$\frac{-4x+25}{4}$$