# How do you solve x^2-x=2?

Jun 28, 2015

Solve $y = {x}^{2} - x - 2 = 0$

#### Explanation:

Since (a - b + c = 0), use shortcut -> One real root is (-1) and the other is (-c/a = 2)

Jun 29, 2015

The solutions are $2$ and $- 1$.

#### Explanation:

To solve: ${x}^{2} - x = 2$,

First we note that this is a quadratic equation. We are used to seeing quadratic equations as: $a {x}^{2} + b x + c = 0$, so let's make the equation in this question look like that:

${x}^{2} - x = 2$, Subtract $2$ (add $- 2$) on both sides)

${x}^{2} - x - 2 = 0$.

Now we have choices, we could try to factor, we could complete the square, we could use the quadratic formula. I like to try to factor first, because if the quadratic factors easily, I find that fastest. But don't spend a lot of time factoring, because we have 2 other methods that will work even if we can't easily find the factorization.

It is fairly straightforward to factor: ${x}^{2} - x - 2$. We get:

$\left(x - 2\right) \left(x + 1\right) = 0$.

$x - 2 = 0$ $\textcolor{w h i t e}{\text{xx}}$ or $\textcolor{w h i t e}{\text{xx}}$ $x + 1 = 0$
$x = 2$ $\textcolor{w h i t e}{\text{xx}}$ or $\textcolor{w h i t e}{\text{xx}}$ $x = - 1$