How do you solve #x^2 + 12x + 20 = 0# by completing the square?
Our Quadratic is in the form
First, let's subtract
Simplifying, we get:
Now, we factor the left side of the equation. We think of two numbers that add up to
We can now factor this as:
Notice, what I have in blue is the same as
Taking the square root of both sides, we get:
By completing the square, we always half the coefficient of
Also by completing the square, we also take away the squared number of half of the previous coefficient (the number in the brackets).
Plugging this back in, removing the
This is in the completed square form. You can always check this by expanding out:
Solving; so far we know:
So we add
As we do not want squares brackets, the opposite of squaring is square rooting, and this cancels out the squared brackets:
Always remember the
As we want
Always remember there are mostly two solutions, as there is a plus and minus on the answer.
But using our squared numbers:
These simplify to: