Solve -{left(3/2right)}^2+33/2+18

$$- { \left( \frac{ 3 }{ 2 } \right) }^{ 2 } +3 \frac{ 3 }{ 2 } +18$$

Evaluate

$$\frac{81}{4}=20.25$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-\frac{9}{4}+\frac{3\times 2+3}{2}+18$$

Multiply 3 and 2 to get 6.

$$-\frac{9}{4}+\frac{6+3}{2}+18$$

Add 6 and 3 to get 9.

$$-\frac{9}{4}+\frac{9}{2}+18$$

Least common multiple of 4 and 2 is 4. Convert -\frac{9}{4} and \frac{9}{2} to fractions with denominator 4.

$$-\frac{9}{4}+\frac{18}{4}+18$$

Since -\frac{9}{4} and \frac{18}{4} have the same denominator, add them by adding their numerators.

$$\frac{-9+18}{4}+18$$

Add -9 and 18 to get 9.

$$\frac{9}{4}+18$$

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

$$\frac{9}{4}+\frac{72}{4}$$

Since \frac{9}{4} and \frac{72}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+72}{4}$$

Add 9 and 72 to get 81.

$$\frac{81}{4}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {2}} = 20\frac{1}{4} = 20.25$$