Complete the Square Calculator

Introduction to Complete the Square Calculator

The Complete the Square calculator with steps is an online tool that is used to make a complete square equation.

Completing the square calculator determines the polynomial quadratic equation to convert it into a standard form of vertex equation and the given equation becomes a complete square in a few seconds.

What is Completing the Square?

Completing the square is an algebraic method that is used for making the quadratic expression into a perfect square equation.

It is a method by which one similar value is added or subtracted from the given quadratic equation and solve by completing the square to make a perfect square equation in the form of a²+b²=(a+b)².

This technique is also applicable when the given quadric equation does not get the solution from factorization and imaginary roots are found from the quadratic formula.

Formula Used by Completing the Square Calculator:

Completing the square formula used to change the quadratic equation into the perfect square equation. Our complete the square calculator uses the following formula to evaluate,

$$ ax^2 + bx + c \Rightarrow a(x + m)^2 $$

$$ m \;=\; \frac{b}{2a} $$

$$ n \;=\; c - \biggr( \frac{b^2}{4a} \biggr) $$

whereas,

ax²+bx+c=0: quadric polynomial equation

a(x+m)²+n: vertex standard form of equation

m = b/2a: (add both sides of the equation)

n = c - (b²/4a): Add and subtract on one side of the equation to make it a perfect square equation

Working Process of Complete the Square Formula Calculator:

Completing the square formula calculator uses the simplest method to calculate the quadratic equation so that you can easily grasp the concept of completing a square in a few seconds. You do not need to do calculations manually or put effort into getting the solution of completing square problems.

You just need to enter the input value in the input field in our completing the square solver and it will start calculating as per your given quadratic equation ax²+bx+c=0.

Let's take an example solution that is given below so that you can easily understand the working method of complete square calculator. Here the given quadratic polynomial equation is x2+4x-5=0 and its roots are a= 1,b= 4, c= -5.

Then completing square calculator applies the formula to change the given equation into a perfect square as b2/4 is added on one side of the equation as (x+b/2)²= x+4x(16/4).

In the same way, b²/4 is subtracted from the root c value from the right side of the equation as (c-b²/4)=-(5 -16/4). After calculation, both sides of an equation become a perfect square (x+b/2)² =(x+4/2)² and (c-b²/4)=9.

Now, our complete the square solver takes the square roots on both sides of the equation to find the root values. After squaring the square equation split into positive and negative values as shown in the below example (x+2)=3, (x+2)=-3.

Then it solves the linear equation and gives the root value as x=1,x=-5. Our complete the square calculator provides a solution of polynomial quadratic equations into a perfect square in no time.

Solved Example Complete the Square:

An example with the solution for the completing a square question is given below which will help you to understand the steps provided by the complete the square formula calculator,

Example:

Calculate the roots of the following quadratic equation by using the completing the square method.

$$ x^2 + 4x - 5 \;=\; 0 $$

Solution:

$$ x^2 + 4x - 5 \;=\; 0 $$

Comparing the equation,

$$ b \;=\; 4, c \;=\; -5 $$

$$ \biggr( x + \frac{b}{2} \biggr)^2 \;=\; -\biggr( c - \frac{b^2}{4} \biggr) $$

So,

$$ \biggr(x+ \frac{4}{2} \biggr)^2 \;=\; -\biggr( 5 - \frac{4^2}{4} \biggr) $$

$$ (x+2)^2 \;=\; 5 + 4 $$

$$ (x+2)^2 \;=\; 9 $$

$$ (x+2) \;=\; \pm \sqrt{9} $$

$$ (x+2) \;=\; \pm 3 $$

$$ x+2 \;=\; 3 $$

$$ x+2 \;=\; -3 $$

$$ x \;=\; 1, -5 $$

How to Use the Complete the Square Calculator?

The completing the square calculator has a feasible design that allows you to easily calculate the polynomial quadratic equation and solve it by completing the square in less than a minute.

You should abide by some of our guidelines before using the complete the square formula calculator for evaluation so that you get a wonderful experience. These guidelines are given as:

1. Enter the differential equation (ax²+bx+c=0) in the input box.
2. Enter the value of a,b,c for the quadric equation in the relevant field.
3. Click the “Calculate” button to get the desired result of your given quadratic equation.
4. If you want to try out our complete square calculator first then you can use the load example so that you become familiar with our tool working process for better clarity about this concept.
5. Check out your input equation before clicking the calculate button so that you do not find any error in the calculation process.
6. Click on the “Recalculate” button to get a new page for solving more Completing the Square problems.

Results from Completing the Square Formula Calculator:

The Complete the Square calculator provides you with the solution to a given polynomial equation problem when you give the input to it. It provides you with solutions in a step-wise process in less than a minute. It may contain the following:

• Result option gives you a solution for Completing the Square question.
• Possible step section provides you with all the steps in the process of the Completing the Square problem.

Advantages of Complete Square Calculator:

Completing square calculator will give you tons of advantages whenever you use it to calculate the polynomial quadratic equation. Its advantages are:

• Our Completing the Square solver saves your time from doing lengthy calculations of the Completing the Square problem.
• The completing the square calculator is a free-of-cost tool so you can use it to find the polynomial expression.
• The complete the square formula calculator is a versatile tool that allows you to solve various types of integral functions or quadratic equations.
• You can use this Complete the Square solver for practice so that you get familiar with the Completing the Square questions.
• It is a reliable tool that provides you with accurate solutions every time whenever you use it to calculate the given quadratic equation.
• The complete the square calculator provides a solution with a complete process in a step-wise process with no or minimal error so that you get a better understanding.