Complete the square calculator

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

ax2bxcaxp2q

where p and q are unknows parameters to be determined.

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

ax2bxcax22pxp2q

and then, open the brackets:

ax2bxcax22apxap2q

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

aab2apcap2q

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:

pb2acab2a2q

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

pb2aqcb24a

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:

ax2bxcaxb2a2cb24a

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
Complete the square for polynomial pxx22x45by using undefinite coefficient method
Input second order polynomial:


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