# How do you factor x+1+2x^2?

Jun 11, 2018

 x+1+2*x^2=(x+(1/2+-sqrt(2)/(2)))*(x-(1/2+-sqrt(2)/(2))

#### Explanation:

The Quadratic Formula: For ax^2" + bx + c = 0, the values of x (factors) which are the solutions of the equation are given by:
$x = \frac{b \pm \sqrt{4 \cdot a \cdot c}}{2 \cdot a}$

Here, a=2, b=1 and c=1, so
$x = \frac{1 \pm \sqrt{4 \cdot 2 \cdot 1}}{2 \cdot 2}$

$= \frac{1 \pm 2 \cdot \sqrt{2}}{4}$

$= \frac{1}{2} \pm \frac{\sqrt{2}}{2}$

You can then factor as follows, using the two factors found:

-> x+1+2*x^2=(x+(1/2+-sqrt(2)/(2)))*(x-(1/2+-sqrt(2)/(2))