Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square. Let's convert to standard form by dividing both sides by 1:
We have: .
What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is 6, we know that 6=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .
The highlighted red part must be equal to -8 (highlighted green part).
, or .
So, the equation converts to , or .
Our equation converted to a square , equated to a number (17).
Since the right part 17 is greater than zero, there are two solutions: