Question

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

Answer 1

See below.

Explanation:

We can factor or graph the equation.

Factoring:
`x^2-x-20=0` becomes `(x-5)(x+4)=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.

Answer 2

See the entire solution process below:

Explanation:

First, subtract `color(red)(20)` from each side of the equation to put this equation into quadratic form:

`x^2 - x - color(red)(20) = 20 - color(red)(20)`

`x^2 - x - 20 = 0`

Because `4 - 5 = -1` and `4 xx -5 = -20` we can factor the left side of the equation as

`(x + 4)(x - 5) = 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 - color(red)(4) = 0 - color(red)(4)`

`x + 0 = -4`

`x = -4`

Solution 2)

`x - 5 = 0`

`x - 5 + color(red)(5) = 0 + color(red)(5)`

`x - 0 = 5`

`x = 5`

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