I am trying to define the different appraoches to solving quadratic equations. My book says using quadratic formula, completing the sqaure and factoring.

Question

I thought completing the square would be by facotring? How are these two different?

Answer 1

Completing the square is a variation, I suppose, of factoring. The idea is to make the number, which isn't factorable (is that a word?) into one that can be factored. For example,
X^2 + 4x + 4 can be factored into (x+2)^2. So if we had an equation, such as
X^2 + 4x + 3, we rearrange the equation to
X^2 + 4x + ..... = -3
Then we add 4 to both sides, like this,
X^2 + 4x + 4 = -3 + 4
Now the left side is a perfect square
(X + 2)^2 = +1
and we solve for X.
I hope this answers your question.