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 z is 15, we know that 15=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 56 (highlighted green part).
 , or  .
So, the equation converts to  , or  .
Our equation converted to a square  , equated to a number (0.25).
Since the right part 0.25 is greater than zero, there are two solutions:
, or
Answer: z=-7, -8.
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