Solve (-1/2n^3+1/2n^2+4.6n)+(-9/4n^3+1/2n^2+4.5n)

$$( - \frac { 1 } { 2 } n ^ { 3 } + \frac { 1 } { 2 } n ^ { 2 } + 4.6 n ) + ( - \frac { 9 } { 4 } n ^ { 3 } + \frac { 1 } { 2 } n ^ { 2 } + 4.5 n )$$

Evaluate

$$-\frac{11n^{3}}{4}+n^{2}+\frac{91n}{10}$$

Solution Steps

Combine -\frac{1}{2}n^{3} and -\frac{9}{4}n^{3} to get -\frac{11}{4}n^{3}.

$$-\frac{11}{4}n^{3}+\frac{1}{2}n^{2}+4.6n+\frac{1}{2}n^{2}+4.5n$$

Combine \frac{1}{2}n^{2} and \frac{1}{2}n^{2} to get n^{2}.

$$-\frac{11}{4}n^{3}+n^{2}+4.6n+4.5n$$

Combine 4.6n and 4.5n to get 9.1n.

$$-\frac{11}{4}n^{3}+n^{2}+9.1n$$

Factor

$$-\frac{13.75n\left(n-\left(-\frac{\sqrt{10110}}{55}+\frac{2}{11}\right)\right)\left(n-\left(\frac{\sqrt{10110}}{55}+\frac{2}{11}\right)\right)}{5}$$