Solve -3/2*51^2+149*51-200

$$- \frac { 3 } { 2 } \times 51 ^ { 2 } + 149 \times 51 - 200$$

Evaluate

$$\frac{6995}{2}=3497.5$$

Solution Steps

Calculate 51 to the power of 2 and get 2601.

$$-\frac{3}{2}\times 2601+149\times 51-200$$

Express -\frac{3}{2}\times 2601 as a single fraction.

$$\frac{-3\times 2601}{2}+149\times 51-200$$

Multiply -3 and 2601 to get -7803.

$$\frac{-7803}{2}+149\times 51-200$$

Fraction \frac{-7803}{2} can be rewritten as -\frac{7803}{2} by extracting the negative sign.

$$-\frac{7803}{2}+149\times 51-200$$

Multiply 149 and 51 to get 7599.

$$-\frac{7803}{2}+7599-200$$

Convert 7599 to fraction \frac{15198}{2}.

$$-\frac{7803}{2}+\frac{15198}{2}-200$$

Since -\frac{7803}{2} and \frac{15198}{2} have the same denominator, add them by adding their numerators.

$$\frac{-7803+15198}{2}-200$$

Add -7803 and 15198 to get 7395.

$$\frac{7395}{2}-200$$

Convert 200 to fraction \frac{400}{2}.

$$\frac{7395}{2}-\frac{400}{2}$$

Since \frac{7395}{2} and \frac{400}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7395-400}{2}$$

Subtract 400 from 7395 to get 6995.

$$\frac{6995}{2}$$

Factor

$$\frac{5 \cdot 1399}{2} = 3497\frac{1}{2} = 3497.5$$