# Completing the Square Calculator

'Cuemath's Completing the Square Calculator' is an online tool that helps to calculate the roots of a given quadratic equation.

## What is Completing the Square Calculator?

Cuemath's online Completing the Square Calculator helps you to calculate the roots of a given quadratic equation within a few seconds.

## How to Use Completing the Square Calculator?

Please follow the below steps to use completing the square calculator:

**Step 1**: Enter the coefficients of A, B, and C in the given input box.**Step 2**: Click on the**"Solve"**button to calculate the roots of the given quadratic equation.**Step 3**: Click on**"Reset"**to clear the field and calculate the roots for different quadratic equations.

## What is Completing the Square Calculator?

Completing the square method is used to solve the quadratic equation in the form ax^{2} + bx + c = 0

Completing the square method is converting a quadratic expression in the form **ax ^{2 }+ bx + c** to the vertex form

**a(x+d)**, where

^{2}+ e**d =b/2a, and e = c - b**

^{2}/(4a)Let's see the below example to understand briefly.

**Solved Example:**

Solve quadratic equation x^{2} + 6x + 7 = 0 using completing square method?

**Solution:**

Given: a = 1, b = 6, c = 7

Converting quadratic expression in the form ax^{2 }+ bx + c = 0 to the vertex form a(x+d)^{2} + e = 0, where d = b/2a, and e = c - b^{2}/(4a)

d = b/2a = 6 / 2 = 3

e = c - b^{2}/(4a) = 7 - 6^{2} / 4 = 7 - 9 = -2

Substitute the d = 3 and e = -2 in the vertex form a(x+d)^{2} + e

1(x + 3)^{2} + (-2) = 0

(x + 3)^{2} = 2

x + 3 = \( \pm \)√2

x = √2 - 3, -√2 - 3

x = -1.59 , -4.41

Similarly, you can try the calculator to find the variable value using completing square method for

a) x^{2} - 10x + 16 = 0

b) x^{2} - 5x + 6 = 0