Solve -5/4-2^33+7/2d_{1}-2^24^2

$$- \frac { 5 } { 4 } - 2 ^ { 3 } 3 + \frac { 7 } { 2 } d _ { 1 } - 2 ^ { 2 } 4 ^ { 2 }$$

Evaluate

$$\frac{7d_{1}}{2}-\frac{357}{4}$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$-\frac{5}{4}-8\times 3+\frac{7}{2}d_{1}-2^{2}\times 4^{2}$$

Multiply 8 and 3 to get 24.

$$-\frac{5}{4}-24+\frac{7}{2}d_{1}-2^{2}\times 4^{2}$$

Convert 24 to fraction \frac{96}{4}.

$$-\frac{5}{4}-\frac{96}{4}+\frac{7}{2}d_{1}-2^{2}\times 4^{2}$$

Since -\frac{5}{4} and \frac{96}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-96}{4}+\frac{7}{2}d_{1}-2^{2}\times 4^{2}$$

Subtract 96 from -5 to get -101.

$$-\frac{101}{4}+\frac{7}{2}d_{1}-2^{2}\times 4^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{101}{4}+\frac{7}{2}d_{1}-4\times 4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{101}{4}+\frac{7}{2}d_{1}-4\times 16$$

Multiply 4 and 16 to get 64.

$$-\frac{101}{4}+\frac{7}{2}d_{1}-64$$

Convert 64 to fraction \frac{256}{4}.

$$-\frac{101}{4}+\frac{7}{2}d_{1}-\frac{256}{4}$$

Since -\frac{101}{4} and \frac{256}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-101-256}{4}+\frac{7}{2}d_{1}$$

Subtract 256 from -101 to get -357.

$$-\frac{357}{4}+\frac{7}{2}d_{1}$$

Factor

$$\frac{7\left(2d_{1}-51\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-357+14d_{1}}{4}$$

Consider -5-96+14d_{1}-256. Multiply and combine like terms.

$$14d_{1}-357$$

Consider 14d_{1}-357. Factor out 7.

$$7\left(2d_{1}-51\right)$$

Rewrite the complete factored expression.

$$\frac{7\left(2d_{1}-51\right)}{4}$$