Step by step
The question
Question: choose a method and solve x² − 5x + 6 = 0.
1 Choose the method
We ask in order.
First: is there no x term?
No, there is one.
x² has no number in front, and two whole numbers work.
So it factors.
So: factoring.
2 Factor
We need two numbers.
They multiply to 6, and they add to −5.
They multiply to a plus number, so the two numbers have the same sign.
They add to a minus number, so both are minus.
We list the pairs that make 6, smallest first.
We add each pair.
We need 5.
2 and 3 give 5.
Yes!
With the signs: −2 and −3.
So it is (x − 2)(x − 3) = 0.
3 One bracket is 0
Two numbers multiply to 0.
That only happens if one of them is 0.
So one bracket must be 0.
We make each bracket 0.
Two small equations.
In x − 2 = 0, we add 2 on both sides.
In x − 3 = 0, we add 3 on both sides.
So x = 2 or x = 3.
4 Check
Let's check: put x = 2 into the left side.
We get 0, the same as the right side.
It works!
Now put x = 3 into the left side.
We get 0 again, the same as the right side.
So both answers are right!
Let's look back.
First: choose the method.
Then: factor.
Then: one bracket is 0.
Last: check.