Complete the Square Calculator

Understand the complete the square calculator result

Use Complete the Square Calculator when you are rewriting a quadratic for graphing, vertex identification, or integration. It asks for coefficient b, constant c and reports shift and outside constant. For x squared plus bx plus c, half of b is placed inside the square and its square is subtracted from c. The output represents x plus the shift, all squared, plus the outside constant. By exposing shift and outside constant, Complete the Square Calculator makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Coefficient b 6, Constant c 5, the verified output is Shift 3, Outside constant -4. If the quadratic begins with another coefficient, factor it from the x terms before using this form. In Complete the Square Calculator, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how shift responds.

Method, limits, and private processing

This focused version assumes the leading coefficient of x squared is one. Complete the Square Calculator evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its shift and outside constant, retain the stated method and input units because this result is bounded by the assumptions of for x squared plus bx plus c, half of b is placed inside the square and its square is subtracted from c.