Step by step
The question
Question: solve x² − 7x + 10 = 0.
1 Factor
We need two numbers.
They multiply to 10, and they add to −7.
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 10, smallest first.
We add each pair.
We need 7.
2 and 5 give 7.
Yes!
With the signs: −2 and −5.
So it is (x − 2)(x − 5) = 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.
Two small equations.
In x − 2 = 0, we add 2 on both sides.
In x − 5 = 0, we add 5 on both sides.
So x = 2 or x = 5.
3 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 = 5 into the left side.
We get 0 again, the same as the right side.
So both answers are right!
Let's look back.
First: factor.
Then: one bracket is 0.
Last: check.