Completing the Square

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Recall the algebraic identity

We can use this to complete the square. Consider the quadratic function

What can be added to yield a perfect square? Compare the coefficients of 


Generalizing to any quadratic function of the form tex2html-wrap-inline74 , 2e=b which yields e=b/2. Hence

Example: Use Complete the Square Method to solve

Note that the method above is for quadratic functions containing tex2html-wrap-inline84 . We divide the equation by 2:

which is equivalent to

In order to generate a perfect square we add  to both sides of the equation

Easy algebraic calculations give

Taking the square-roots lead to


which give the solutions to the equation:


See also the quadratic formula.


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