Completing the Square Calculator

Completing the Square Calculator is a free online tool that uses the completing the square method to display the variable value for the quadratic equation. This online completing the square calculator from Mathematics Master speeds up calculations and shows the variable value almost instantly.

Please provide values for \( ax^2 + bx + c = 0 \)

How to Use the Completing the Square Calculator?

  • Fill out the input field with the expression.
  • To get the result, click the solve button
  • Finally, the output will display the variable value for the specified term.

What is Completing the Square?

The quadratic equation is resolved in mathematics using the completing the square approach. In this approach, we modify the given equation’s form so that the left side should be a perfect square binomial. This approach requires that the equation take the form \( ax^2+ bx+ c=0 \). Completing the square method helps solve quadratic equations that can’t be solved using quadratic formulas.

Methods of finding solutions to Quadratic Equation

A quadratic equation’s root or solution is essentially a number that satisfies the equation. The value on the right side of the equation will be equal to the value on the left side if we substitute the number on the left side.

Any quadratic equation can be solved using one of three methods:

  • Factoring approach
  • Completing the square method
  • Quadratic formula method

The factoring approach is one of the fundamental methods for solving a quadratic equation. However, this approach is only helpful for a particular class of quadratic equations. On the other hand, we can use the quadratic formula and complete the square procedures to resolve almost all varieties of quadratic problems. Moreover, the completing square technique is helpful because not all such equations can be factored in.


What is Completing the Square?

Writing a quadratic expression containing the perfect square is known as “completing the square” in algebra. In other words, the act of “completing the square” can be described as taking the quadratic equation “\(ax^2 + bx + c = 0\)” and changing it to “\(a(x + p)^2 + q = 0\).” This approach is used to find the quadratic equation’s roots.

How to complete the square?

  • Write the quadratic equation as \( x^2 + bx + c \) (The coefficient of \( x^2\) must be 1).
  • Calculate the other half of the x-coefficient.
  • Square the result of step 1’s calculation.
  • Adjust the \(x^2\) term by adding and subtracting the square from step 2.
  • Factorize the polynomial and complete the square by using the algebraic formula \( x^2 + 2xy + y^2 = (x + y)^2\).

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