Question

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

Answer 1

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)

Answer 2

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: `ax^2 + bx + 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:

`(x-2) (x +1) = 0`.

That leads to

`x-2 =0` `color(white)"xx"` or `color(white)"xx"` `x+1 =0`

`x = 2` `color(white)"xx"` or `color(white)"xx"` `x = -1`