Complete the Square Calculator

The Complete the Square Calculator is a valuable tool used in algebra to transform a quadratic equation into its completed square form. This method is particularly useful for solving quadratic equations, as it simplifies the process by allowing you to easily identify the vertex of the parabola represented by the equation.

How to Use:

  1. Enter Coefficients: Input the coefficients of the quadratic equation ( ax^2 + bx + c = 0 ) into the respective fields:
    • ( a ): Coefficient of ( x^2 )
    • ( b ): Coefficient of ( x )
    • ( c ): Constant term
  2. Click "Complete the Square": After entering the coefficients, click the "Complete the Square" button to initiate the calculation.
  3. View Completed Square Form: The calculator will process the input coefficients and display the quadratic equation in its completed square form: ( (x + p)^2 + q ), where ( p ) and ( q ) are constants.

Note: If the equation has complex roots, a message indicating this will be displayed.

Example:

  • Suppose we have the quadratic equation ( 2x^2 - 8x + 5 = 0 ).
  • Using the Complete the Square Calculator, we input ( a = 2 ), ( b = -8 ), and ( c = 5 ).
  • Upon calculation, the completed square form will be displayed as ( (x - 2)^2 + 1 ).

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