Step by step
The question
Question: solve x² − 6x + 9 = 0.
1 Factor
We need two numbers.
They multiply to 9, and they add to −6.
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 9, smallest first.
We add each pair.
We need 6.
3 and 3 give 6.
Yes!
With the signs: −3 and −3.
So it is (x − 3)(x − 3) = 0.
2 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.
The two brackets are the same.
In x − 3 = 0, we add 3 on both sides.
Both brackets give the same answer.
So there is only one answer: x = 3.
3 Check
Let's check: put x = 3 into the left side.
We get 0, the same as the right side.
It works!
Let's look back.
First: factor.
Then: one bracket is 0.
Last: check.