Solve (-9/2)^2+9(-9/2)+18

$$( - \frac { 9 } { 2 } ) ^ { 2 } + 9 ( - \frac { 9 } { 2 } ) + 18$$

Evaluate

$$-\frac{9}{4}=-2.25$$

Solution Steps

Calculate -\frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$\frac{81}{4}+9\left(-\frac{9}{2}\right)+18$$

Express 9\left(-\frac{9}{2}\right) as a single fraction.

$$\frac{81}{4}+\frac{9\left(-9\right)}{2}+18$$

Multiply 9 and -9 to get -81.

$$\frac{81}{4}+\frac{-81}{2}+18$$

Fraction \frac{-81}{2} can be rewritten as -\frac{81}{2} by extracting the negative sign.

$$\frac{81}{4}-\frac{81}{2}+18$$

Least common multiple of 4 and 2 is 4. Convert \frac{81}{4} and \frac{81}{2} to fractions with denominator 4.

$$\frac{81}{4}-\frac{162}{4}+18$$

Since \frac{81}{4} and \frac{162}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-162}{4}+18$$

Subtract 162 from 81 to get -81.

$$-\frac{81}{4}+18$$

Convert 18 to fraction \frac{72}{4}.

$$-\frac{81}{4}+\frac{72}{4}$$

Since -\frac{81}{4} and \frac{72}{4} have the same denominator, add them by adding their numerators.

$$\frac{-81+72}{4}$$

Add -81 and 72 to get -9.

$$-\frac{9}{4}$$

Factor

$$-\frac{9}{4} = -2\frac{1}{4} = -2.25$$