Step by step
The question
Question: choose a method and solve x² + 6x + 9 = 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 9, and they add to 6.
They multiply to a plus number, so the two numbers have the same sign.
They add to a plus number, so both are plus.
We list the pairs that make 9, smallest first.
We add each pair.
We need 6.
3 and 3 give 6.
Yes!
So it is (x + 3)(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.
The two brackets are the same.
In x + 3 = 0, we take away 3 on both sides.
Both brackets give the same answer.
So there is only one answer: x = −3.
4 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: choose the method.
Then: factor.
Then: one bracket is 0.
Last: check.