Completing the square
Completing the square is a technique of elementary algebra wherein an expression
is replaced by one of the form
Specifically, we have
See quadratic formula for the application to the problem of solving the quadratic equation.
Example
Consider the problem of finding this antiderivative:
The denominator is
Adding (10/2)2 = 25 to x2 - 10x gives a perfect square x2 - 10x + 25 = (x - 5)2. So we get
Our integral becomes
Completing the square reduces any problem involving a quadratic polynomial to one involving a quadractic polynomial with no 1st-degree term.
Referenced By
List of mathematical topics | List of mathematical topics (A-C) | List of mathematics topics | List of polynomial topics
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