Complete the square calculator

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

Complete square formula with unknown parameters

where p and q are unknows parameters to be determined.

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

square

and then, open the brackets:

Open the brackets

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

System of equations to determine unknown parameters for complete square formula

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:

System of equations to determine unknown parameters for complete square formula

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

Values of unknown parameters for complete square formula

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:

Completing the square formula

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
Second degree polynomial
Input second order polynomial:


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