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jmc

algebra senior

Problem

Marina solved the quadratic equation by completing the square. In the process, she came up with the equivalent equation where and are constants.

What is ?
Solution
Dividing both sides of the equation by , we have The square which agrees with except for the constant term is , which is equal to and thus to .

Therefore, by adding to each side, Marina rewrote the equation as We have and .
Final answer
81