Completing the square calculator

A Worked example to illustrate how the complete square calculator Works:

This calculator will solve second order polynomials using the completing square method. The completing square method is a classical technique of finding the roots of quadratic equations. A quadratic equation of the form ax² + bx + c = 0 for x, where a ≠ 0 can be solved online using the equation calculator. As the name suggest, the completing square method aims to solve quadratics by creating a perfect square on the variable side. It is easy to reduce a perfect square equation to degree 1 simply by taking the square roots on either side.

Unlike other generic online calculators, this calculator will show you all the steps.  A quadratic equation has two roots, which can either be real or complex. The calculator solves for both complex and real roots.

Complete the square steps

To solve an equation through this method, first you have to put the equation in standard form. This means setting the first constant “a =1’ by dividing all through by ‘a’.

Let solve the Following equation By Completing Square method to illustrate the basic steps.

2x^2 - 6x + 7 = 0

a \ne 1, a = 2, so we can devide through by 2

\frac{2}{2}x^2 - \frac{6}{2}x +  \frac{7}{2} = \frac{0}{2}

Dividing by 2 yields

x^2 - 3x + \frac{7}{2} = 0

We can no proceed and complete the square:

x^2 - 3x - \frac{9}{4} + \frac{7}{2} +\frac{9}{4} = 0  (Add and subtract (\frac{b}{2})^2

(x- \frac{3}{2})^2 = \frac{-23}{4}

x- \frac{3}{2})= \pm\sqrt{\frac{-23}{4}}=\pm\frac{\sqrt{-23}}{2}

thus x= \frac{3}{2}- \frac{\sqrt{-23}}{2} Or x= \frac{3}{2}+ \frac{\sqrt{-23}}{2}

From the example above, it is sufficient to create perfect square on the LHS of the equation in order to solve it with the completing square method.

How the Completing Square Calculator Works

The online calculator uses fundamental techniques to solve math problems through completing square method. To get started, enter math text in the text area provided. Click on the Calculate Button to get solution. The calculator will give you step by step solution.

Here are more completing square examples to illustrate how the calculator Works.