# How do you find the roots of #x^2-x=6#?

##### 2 Answers

#### Explanation:

Write as

Notice that

And that

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We need the product (multiplication answer) to be negative (-6)

So either 3 is negative and 2 positive or the other way round as

But the

So if

So we have to have

The solutions/roots to

#### Explanation:

We have

We need to put this in standard form (

with

You have three ways of solving a quadratic equation:

1) Use the quadratic formula,

where

2) Factor, for simple equations with

3) Directly solve the equation by first completing the square to get the expression into vertex form, (or perhaps it's already in vertex form?) then solving the resulting equation (any solvable quadratic equation can be directly solved from vertex form, this is how the quadratic formula is proven).

Since these numbers are simple and method 1 is just plug-in and method 3 is rather obscure unless you're already in vertex form (or something close to it), I will use method 2.

We have

we are looking for factors of

We consider

1st try,

2nd try,

3rd try,

4th try,

this means are factors are

our expression becomes

(if you expand this expression you will reproduce

We find

so

We find

so

The solutions/roots to