Solve 1-3x-6x^2

$$1 - 3 x - 6 x ^ { 2 }$$

Factor

$$-6\left(x-\left(-\frac{\sqrt{33}}{12}-\frac{1}{4}\right)\right)\left(x-\left(\frac{\sqrt{33}}{12}-\frac{1}{4}\right)\right)$$

Steps Using the Quadratic Formula

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.

$$-6x^{2}-3x+1=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-6\right)}}{2\left(-6\right)}$$

Square -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-6\right)}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{-\left(-3\right)±\sqrt{9+24}}{2\left(-6\right)}$$

Add 9 to 24.

$$x=\frac{-\left(-3\right)±\sqrt{33}}{2\left(-6\right)}$$

The opposite of -3 is 3.

$$x=\frac{3±\sqrt{33}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{3±\sqrt{33}}{-12}$$

Now solve the equation x=\frac{3±\sqrt{33}}{-12} when ± is plus. Add 3 to \sqrt{33}.

$$x=\frac{\sqrt{33}+3}{-12}$$

Divide 3+\sqrt{33} by -12.

$$x=-\frac{\sqrt{33}}{12}-\frac{1}{4}$$

Now solve the equation x=\frac{3±\sqrt{33}}{-12} when ± is minus. Subtract \sqrt{33} from 3.

$$x=\frac{3-\sqrt{33}}{-12}$$

Divide 3-\sqrt{33} by -12.

$$x=\frac{\sqrt{33}}{12}-\frac{1}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{1}{4}-\frac{\sqrt{33}}{12} for x_{1} and -\frac{1}{4}+\frac{\sqrt{33}}{12} for x_{2}.

$$-6x^{2}-3x+1=-6\left(x-\left(-\frac{\sqrt{33}}{12}-\frac{1}{4}\right)\right)\left(x-\left(\frac{\sqrt{33}}{12}-\frac{1}{4}\right)\right)$$

Evaluate

$$1-3x-6x^{2}$$