Search for a tool
Completing the Square

Tool to make automatic square completion. The square completion is a calculation method allowing to factor a quadratic polynomial expression using polynomial depression.

Results

Completing the Square -

Tag(s) : Mathematics,Symbolic Computation

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Completing the Square tool. Thank you.

This page is using the new English version of dCode, please make comments !

Completing the Square

Sponsored ads

This script has been updated, please report any problems.

Completing the square solver



Tool to make automatic square completion. The square completion is a calculation method allowing to factor a quadratic polynomial expression using polynomial depression.

Answers to Questions

How to complete the square?

dCode can complete the square by depressing a polynomial expression

Let P be $$ x^2 +bx + c = 0 $$ one adds $$ (b/2)^2 - c - (b/2)^2 + c$$ that allows factorizing P in $$ (x +(b/2))^2 - (b/2)^2 + c$$

dCode can generalize the approach to degrees n superior to 2 by removing the term of degree n-1.

Here is a practical example for a completion by hand: $$ p(x) = 2x ^ 2 + 12x + 14 $$

Factorize the coefficienthref \( x ^ 2 \) \( p(x) = 2 (x ^ 2 + 6x + 7) \) and continue with \( x ^ 2 + 6x + 7 \)

Identify the coefficient of \( x \) here 6 and divide it by 2 to get \( β = 6/2 = 3 \)

Use \( β \) to write $$ x ^ 2 + 6x + 7 = (x + 3) ^ 2-β ^ 2 + 7 = (x + 3) ^ 2-2 $$

Multiply everything by the coefficient found previously (2) to obtain the completed square: $$ p(x) = 2x ^ 2 + 12x + 14 = 2 ((x + 3) ^ 2-2) = 2 (x + 3 ) ^ 2-6 $$

Ask a new question

Source code

dCode retains ownership of the source code of the script Completing the Square. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Completing the Square script for offline use, for you, your company or association, see you on contact page !

Questions / Comments


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Completing the Square tool. Thank you.


Source : http://www.dcode.fr/square-completion
© 2016 dCode — The ultimate 'toolkit' website to solve every problem. dCode