How do you solve the quadratic equation by completing the square: #x^2 - 20x = 0#?
Completing the square is just like it sounds, you are looking for a number that makes your quadratic a perfect square so it can be written as
The way to do this is by understanding the distributive property and how it gives you that number that makes a perfect square. So let us write out the expression
Notice that there is a
You should also notice that the
This means that
So to make
it looks like we added 100 to make it a perfect square. To keep the equation balanced we need to add 100 to the other side of the equation.
but now you can factor the quadratic on the left using the
and taking the square root of both sides
which is what you would have obtained if you had just factored out the greatest common factor (
But that is the why and the how of completing the square.