Solve x^4+7^4+x(-x)/24

$$x ^ { 4 } + 7 ^ { 4 } + \frac { x ( - x ) } { 24 }$$

Evaluate

$$x^{4}-\frac{x^{2}}{24}+2401$$

Short Solution Steps

Calculate 7 to the power of 4 and get 2401.

$$x^{4}+2401+\frac{x\left(-x\right)}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}+2401 times \frac{24}{24}.

$$\frac{24\left(x^{4}+2401\right)}{24}+\frac{x\left(-x\right)}{24}$$

Since \frac{24\left(x^{4}+2401\right)}{24} and \frac{x\left(-x\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{24\left(x^{4}+2401\right)+x\left(-x\right)}{24}$$

Do the multiplications in 24\left(x^{4}+2401\right)+x\left(-x\right).

$$\frac{24x^{4}+57624-x^{2}}{24}$$

Factor

$$\frac{24x^{4}-x^{2}+57624}{24}$$

Solution Steps

Factor out \frac{1}{24}. Polynomial 24x^{4}+57624-x^{2} is not factored since it does not have any rational roots.

$$\frac{24x^{4}+57624-xx}{24}$$