Solve 5^3-3s^2+3s-9

$$5 ^ { 3 } - 3 s ^ { 2 } + 3 s - 9$$

Evaluate

$$116+3s-3s^{2}$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$125-3s^{2}+3s-9$$

Subtract 9 from 125 to get 116.

$$116-3s^{2}+3s$$

Factor

$$-3\left(s-\left(-\frac{\sqrt{1401}}{6}+\frac{1}{2}\right)\right)\left(s-\left(\frac{\sqrt{1401}}{6}+\frac{1}{2}\right)\right)$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 3 and get 125.

$$factor(125-3s^{2}+3s-9)$$

Subtract 9 from 125 to get 116.

$$factor(116-3s^{2}+3s)$$

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-3s^{2}+3s+116=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$s=\frac{-3±\sqrt{3^{2}-4\left(-3\right)\times 116}}{2\left(-3\right)}$$

Square 3.

$$s=\frac{-3±\sqrt{9-4\left(-3\right)\times 116}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$s=\frac{-3±\sqrt{9+12\times 116}}{2\left(-3\right)}$$

Multiply 12 times 116.

$$s=\frac{-3±\sqrt{9+1392}}{2\left(-3\right)}$$

Add 9 to 1392.

$$s=\frac{-3±\sqrt{1401}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$s=\frac{-3±\sqrt{1401}}{-6}$$

Now solve the equation s=\frac{-3±\sqrt{1401}}{-6} when ± is plus. Add -3 to \sqrt{1401}.

$$s=\frac{\sqrt{1401}-3}{-6}$$

Divide -3+\sqrt{1401} by -6.

$$s=-\frac{\sqrt{1401}}{6}+\frac{1}{2}$$

Now solve the equation s=\frac{-3±\sqrt{1401}}{-6} when ± is minus. Subtract \sqrt{1401} from -3.

$$s=\frac{-\sqrt{1401}-3}{-6}$$

Divide -3-\sqrt{1401} by -6.

$$s=\frac{\sqrt{1401}}{6}+\frac{1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{2}-\frac{\sqrt{1401}}{6} for x_{1} and \frac{1}{2}+\frac{\sqrt{1401}}{6} for x_{2}.

$$-3s^{2}+3s+116=-3\left(s-\left(-\frac{\sqrt{1401}}{6}+\frac{1}{2}\right)\right)\left(s-\left(\frac{\sqrt{1401}}{6}+\frac{1}{2}\right)\right)$$