The process for finding the last term of a perfect square trinomial (x² +b*x +c) is called completing the square. ‘Completing The Square Calculator' means the calculator is using the process called completing the square. In a perfect square trinomial the last term c is always (.5*b )². One can input the trinomial on the calculator screen as an equation like A*x² +B*x +C = 0 following calculator manual instructions. Calculator then stores the values of coefficients A, B, and C and then simplifies the equation to the form x² +b*x +c = 0. Then the calculator uses the completing the square rule to solve the equation. If the equation is not a perfect square addition, subtraction, division, factoring, and complete the square algebraic operations are done to solve the trinomial equation. Equation in calculator is entered as Ax^Ù2 + Bx + C = 0. When the input equation is not a perfect square then the algebraic operations are done to convert the equation so that the left hand side (LHS) of the equation is a perfect square trinomial (x² +b*x +c; Öc = .5*b) and right hand side RHS) is also a perfect square number d². Once this is done, then x + c = d; x + c = -d. and x = d-c; x = -d-c. Thus the calculator has used the process called completing the square. The calculator also displays the steps done to solve the problem if requested.        

         Completing The Square Calculator

            Steps:

            Divide equation by GCF, ignore GCF, then divide by the coefficient of x²

            Move the constant term to the right

            Square the (.5*b )² and add to both sides of the equation.

            Move the LHS constant to the right

            Then left side is a perfect square trinomial (x +c ) (x-c)

            Take the square root of RHS constant  (Ö d )² .

            x = Ö d –c; x = Ö d +c

            Example 

                        50x² + -20x + -6 = 0

                        2(-3 + -10x + 25x²) = 0

                        -3 + -10x + 25x² = 0

                        -0.12 + -0.4x + x² = 0

                        -0.4x + x² = 0 + 0.12

                        -0.4x + 0.04 + x² = 0.12 + 0.04

                        0.04 + -0.4x + x² = 0.16

                        x + -0.2)(x + -0.2) = 0.16 = (.4 * .4)

                        x + -0.2 = 0.4; x =.6

                        x = -0.4 + 0.2; x = -.2

Algebra is an integral part of mathematics and it involves various tools and techniques. completing the square calculator is one of these techniques that require information of a square derived from a rectangle which is evident from the name itself. This is one of the techniques that have plenty of applications besides its relevance in geometry. Integration or integral calculus is the vital component that requires incorporation of completing the square method. Well, the method of completing the square is not so complex. It involves conversion of a non perfect square trinomial to a perfect square. You can apply this technique only when you have an equation of the order of quadratic form. This kind of equation must satisfy some set of rules, which being it must be set to zero.

You may recall quadratic equation as most of you might have learned them during your high school. Besides, completing the square calculator is an essential part of the curriculum in these grades. A perfect square trinomial consists of a leading coefficient, a constant term and a middle coefficient. In such an equation the middle coefficient of the equation is equivalent to double the product of the square root terms of leading coefficients and the constant term. Once you get through completing the square method, you can easily solve any other quadratic equation as well. No matter whether the equation can be factorized or not, you can still solve it. Another benefit associated to solving completing the square is that you would not require resorting to quadratic formula at the end to solve this equation.

Well, you may have got a fair idea what such methodology encompasses. All that you are required to derive is the equation of the form that is a perfect square trinomial. It requires you to isolate both the terms to each side of the equation as in extract the term ‘x' on one side of the equation while extracting the other constant term on the another side. Divide the middle coefficient into two halves and take half of the coefficient. Next, perform the square of it and finally add it to either sides of the equation. Factorize the equation such that the sign of the equation must be in accordance with the sign of the middle coefficient.

To finish completing the square you need to take square root of the either side of the equation and go for adding and subtracting the constant term on either sides of the equation. And with this you are through with the method, wasn't it easy?