The problem of completing the square is to transform a second order degree polynomial as follows:

where p and q are unknows parameters to be determined.

To determine unknown parameters p and q, transform the equality above as follows:

and then, open the brackets:

To maintain the correct equality, equate the coefficients at the same degrees:

The first equation of the system is the correct identity for any values of a, so it can be excluded. From the second equation, find the parameter p and substitute the resulting expression into the third equation:

Simplify third equation and find the value of the parameter q:

Substitute values of parameters
p
and
q
into the first equation at the top of the page and get the formula for
*completing the square*
of second order degree polynomial:

The problem of completing the square often occurs when solving problems of rational functions integration. Moreover, by solving the problem of completing the square, one can obtain a formula for solving quadratic equations.

Our online calculator completes the square for second order degree polynomial with step by step solution.

Complete the square calculator

Input second order polynomial:

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