How do you find the roots of #x^2-x=6#?
2 Answers
Explanation:
Write as
Notice that
And that
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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