Solve -0125x^3+15x^2-x-12

$$-0125 { x }^{ 3 } +15 { x }^{ 2 } -x-12$$

Evaluate

$$15x^{2}-x-12$$

Solution Steps

Multiply 0 and 125 to get 0.

$$0x^{3}+15x^{2}-x-12$$

Anything times zero gives zero.

$$0+15x^{2}-x-12$$

Subtract 12 from 0 to get -12.

$$-12+15x^{2}-x$$

Factor

$$15\left(x-\frac{1-\sqrt{721}}{30}\right)\left(x-\frac{\sqrt{721}+1}{30}\right)$$

Steps Using the Quadratic Formula

Multiply 0 and 125 to get 0.

$$factor(0x^{3}+15x^{2}-x-12)$$

Anything times zero gives zero.

$$factor(0+15x^{2}-x-12)$$

Subtract 12 from 0 to get -12.

$$factor(-12+15x^{2}-x)$$

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.

$$15x^{2}-x-12=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 15\left(-12\right)}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{-\left(-1\right)±\sqrt{1-60\left(-12\right)}}{2\times 15}$$

Multiply -60 times -12.

$$x=\frac{-\left(-1\right)±\sqrt{1+720}}{2\times 15}$$

Add 1 to 720.

$$x=\frac{-\left(-1\right)±\sqrt{721}}{2\times 15}$$

The opposite of -1 is 1.

$$x=\frac{1±\sqrt{721}}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{1±\sqrt{721}}{30}$$

Now solve the equation x=\frac{1±\sqrt{721}}{30} when ± is plus. Add 1 to \sqrt{721}.

$$x=\frac{\sqrt{721}+1}{30}$$

Now solve the equation x=\frac{1±\sqrt{721}}{30} when ± is minus. Subtract \sqrt{721} from 1.

$$x=\frac{1-\sqrt{721}}{30}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1+\sqrt{721}}{30} for x_{1} and \frac{1-\sqrt{721}}{30} for x_{2}.

$$15x^{2}-x-12=15\left(x-\frac{\sqrt{721}+1}{30}\right)\left(x-\frac{1-\sqrt{721}}{30}\right)$$