Solve 7-3{left(5/2right)}^2+6

$$7-3 { \left( \frac{ 5 }{ 2 } \right) }^{ 2 } +6$$

Evaluate

$$-\frac{23}{4}=-5.75$$

Solution Steps

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$7-3\times \frac{25}{4}+6$$

Express 3\times \frac{25}{4} as a single fraction.

$$7-\frac{3\times 25}{4}+6$$

Multiply 3 and 25 to get 75.

$$7-\frac{75}{4}+6$$

Convert 7 to fraction \frac{28}{4}.

$$\frac{28}{4}-\frac{75}{4}+6$$

Since \frac{28}{4} and \frac{75}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-75}{4}+6$$

Subtract 75 from 28 to get -47.

$$-\frac{47}{4}+6$$

Convert 6 to fraction \frac{24}{4}.

$$-\frac{47}{4}+\frac{24}{4}$$

Since -\frac{47}{4} and \frac{24}{4} have the same denominator, add them by adding their numerators.

$$\frac{-47+24}{4}$$

Add -47 and 24 to get -23.

$$-\frac{23}{4}$$

Factor

$$-\frac{23}{4} = -5\frac{3}{4} = -5.75$$