SOLUTION: Please help me solve by completing the square: x^2 + 15 x = -56

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Question 695874: Please help me solve by completing the square:
x^2 + 15 x = -56
Answer by mouk(232)   (Show Source): You can put this solution on YOUR website!


Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
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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