SOLUTION: I would like to know why the quadratic equation works? What is the proof for it? I see it online but I don't seem to understand it. Thanks

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Question 961595: I would like to know why the quadratic equation works? What is the proof for it? I see it online but I don't seem to understand it. Thanks
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Why a quadratic equation works is because it can be solved. What you ask is uncertain. An expression is equated to another expression, and one of the terms of either expression is a variable squared, either or both of the expressions may contain a linear term for the variable and a constant term. That makes a quadratic equation. Why the general form of any such equation is solvable is based on Completing the Square, in case the general form of the equation were not factorable.

You can see two lessons about that here:
What does Completing the Square mean?
and
Completing the Square for Solving a Quadratic Equation