Step by step
The question
Question: solve x² + 6x = 7.
1 Get 0 on one side
To solve it, we want 0 on the right side.
So we take away 7 on both sides.
We do it on both sides, so they stay equal.
Now we have x² + 6x − 7 = 0.
2 Factor
We need two numbers.
They multiply to −7, and they add to 6.
They multiply to a minus number, so one number is plus and one is minus.
They add to a plus number, so the bigger one is plus.
We list the pairs that make 7, smallest first.
We take the smaller from the bigger.
We need 6.
1 and 7 give 6.
Yes!
With the signs: −1 and 7.
So it is (x − 1)(x + 7) = 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 − 1 = 0, we add 1 on both sides.
In x + 7 = 0, we take away 7 on both sides.
So x = 1 or x = −7.
4 Check
Let's check: put x = 1 into the left side.
We get 7, the same as the right side.
It works!
Now put x = −7 into the left side.
We get 7 again, the same as the right side.
So both answers are right!
Let's look back.
First: get 0 on one side.
Then: factor.
Then: one bracket is 0.
Last: check.