Let's walk through a couple of them together, to go through the process and make sure it makes sense to you.
1. x^2 - 6x + 9 = 0
We know we're going to have (x- ) and (x- ) because the first sign in our quadratic is negative and the second one is positive.
Then, we need two numbers that add together to make -6 and multiply together to make +9.
The only two that work are -3 and -3. This one's not too bad.
We have (x-3)(x-3) = 0 meaning x=3.
We can FOIL this one out to confirm that it works, OR we can plug in x=3 to make sure it works.
2. x^2 - 9x + 14
Again, we have a - and then a +, so we'll have (x- ) and (x- )
We have two numbers that add together to make -9 and multiply together to make +14.
The numbers are going to be -2 and -7
(x-2)(x-7) = 0 meaning x=2 or 7
We can check this one using FOIL or plugging in 2 or 7 for x and confirming that it works.
3. x^2 + 7x - 60
Since we have + and then -, we have (x+ ) and (x- )
We have two numbers that add together to make 7 and multiply together to make -60.
This means one is positive and one is negative, and the bigger one MUST be positive in order for the sum of the two to be positive 7.
(x+12)(x-5) = 0, giving us values for x of and +5.
Again, we can check using either FOIL or plugging the two values in.
Does the process make sense??