# How do you find the roots of x^2-x=20?

Apr 2, 2017

See below.

#### Explanation:

We can factor or graph the equation.

Factoring:
${x}^{2} - x - 20 = 0$ becomes $\left(x - 5\right) \left(x + 4\right) = 0$
So $x = 5 , - 4$.

Graphing:
graph{x^2-x-20 [-4.335, 5.665, -2.06, 2.94]}
We see that the graph intersects the $x$-axis at $x = 5 , - 4$, so those are our roots.

Apr 2, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{20}$ from each side of the equation to put this equation into quadratic form:

${x}^{2} - x - \textcolor{red}{20} = 20 - \textcolor{red}{20}$

${x}^{2} - x - 20 = 0$

Because $4 - 5 = - 1$ and $4 \times - 5 = - 20$ we can factor the left side of the equation as

$\left(x + 4\right) \left(x - 5\right) = 0$

Now, we solve each term on the right side of the equation to find the roots for this problem:

Solution 1)

$x + 4 = 0$

$x + 4 - \textcolor{red}{4} = 0 - \textcolor{red}{4}$

$x + 0 = - 4$

$x = - 4$

Solution 2)

$x - 5 = 0$

$x - 5 + \textcolor{red}{5} = 0 + \textcolor{red}{5}$

$x - 0 = 5$

$x = 5$

The roots are: $x = - 4$ and $x = 5$