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File:Completing the square.svg

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Description
English: Geometric derivation of completing the square.
Date
Source Own work
Author Krishnavedala
SVG development
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This vector image was created with LaTeX.
Source code
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LaTeX code

Source code 
\documentclass[10pt,border=1pt,crop,multi=false,tikz,class=scrartcl]{standalone}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{mathtools}

\usetikzlibrary{arrows,shapes,calc,positioning}

\begin{document}
  \begin{tikzpicture}[>=stealth,semithick,auto,remember picture]
    \node at (0,0) (b1) {Completing the Square};
    \node [rectangle,draw=green!60!black] at (0,-.5) (b2) {$x^2+bx=a$};
    \node [below=1em of b2] (b3) {
    	\begin{tikzpicture}
    		\draw [fill=gray!70] (0,-.5) -- ++(0,1) node [pos=.5,left] {$x$} 
			-- ++(1,0) -- ++(0,-1) -- ++(-1,0) node [pos=.5,below] {$x$};
		\node at (1.25,.25) {$+$};
		\draw [fill=gray!70] (1.5,-.5) -- ++(0,1) -- ++(.5,0) -- ++(0,-1) node [pos=.5,right] {$x$}
			-- ++(-.5,0) node [pos=.5,below] (b31) {$b$};
		\draw [dashed] (1.75,-.5) -- ++(0,1);
		\node at (2.6,0.15) {$=$};
		\node [fill=gray!70,ellipse,minimum width=2em] at (3.25,0.25) {$a$};
    	\end{tikzpicture}
	};
    \node [below=.5em of b3] (b4) {
    	\begin{tikzpicture}
    		\draw [fill=gray!70] (0,-.5) -- ++(0,1) node [pos=.5,left] {$x$} 
			-- ++(1,0) -- ++(0,-1) -- ++(-1,0) node [pos=.5,below] {$x$};
		\node at (1.25,.25) {$+$};
		\draw [fill=gray!70] (1.5,-.5) -- ++(0,1) node [pos=1] (b41) {}
			-- ++(.25,0) -- ++(0,-1) node [pos=.5,right] {$x$}
			-- ++(-.25,0) node [pos=.5,below] (b43) {$\frac{b}{2}$};
		\node at (2.25,.25) {$+$};
		\draw [fill=gray!70] (2.5,-.5) -- ++(0,1) node [pos=1] (b42) {} 
			-- ++(.25,0) -- ++(0,-1) node [pos=.5,right] {$x$}
			-- ++(-.25,0) node [pos=.5,below] (b44) {$\frac{b}{2}$};
		\draw [dashed] (1.75,-.5) -- ++(0,1);
		\node at (3.3,0.15) {$=$};
		\node [fill=gray!70,ellipse,minimum width=2em] at (3.9,0.25) {$a$};
    	\end{tikzpicture}
	};
    \node [below=.5em of b4] (b5) {
    	\begin{tikzpicture}
    		\draw [fill=gray!70] (0,-.5) -- ++(0,1) node [pos=.5,left] {$x$} 
			-- ++(1,0) -- ++(0,-1) -- ++(-1,0) node [pos=.5,below] {$x$};
    		\draw [fill=gray!70] (0,.65) -- ++(0,.25) node [pos=.5,left] {$\frac{b}{2}$} 
			-- ++(1,0) node [pos=.5,above] (b51) {} -- ++(0,-.25) -- ++(-1,0);
    		\draw [fill=gray!70] (1.15,-.5) -- ++(0,1) -- ++(.25,0) 
			-- ++(0,-1) node [pos=.5,above] (b52) {} -- ++(-.25,0) node [pos=.5,below] {$\frac{b}{2}$};
		\node at (1.75,.15) {$=$};
		\node [fill=gray!70,ellipse,minimum width=2em] at (2.4,0.25) {$a$};
    	\end{tikzpicture}
	};
    \node [below=.1em of b5] (b6) {
    	\begin{tikzpicture}
    		\draw [fill=gray!70] (0,-.5) -- ++(0,1) node [pos=.5,left] {$x$} 
			-- ++(1,0) -- ++(0,-1) -- ++(-1,0) node [pos=.5,below] {$x$};
    		\draw [fill=gray!70] (0,.65) -- ++(0,.25) node [pos=.5,left] {$\frac{b}{2}$} 
			-- ++(1,0) node [pos=.5,above] (b61) {} -- ++(0,-.25) -- ++(-1,0);
    		\draw [fill=gray!70] (1.15,-.5) -- ++(0,1) -- ++(.25,0) 
			-- ++(0,-1) node [pos=.5,above] (b62) {} -- ++(-.25,0) node [pos=.5,below] {$\frac{b}{2}$};
		\draw [fill=blue!70] (1.15,.65) -- ++(0,.25) -- ++(.25,0) -- ++(0,-.25) -- ++(-.25,0);
		\node at (1.75,.15) {$=$};
		\node [fill=gray!70,ellipse,minimum width=2em] at (2.4,0.25) {$a$};
		\node at (3,.25) {$+$};
		\draw [fill=blue!70] (3.25,-.125) -- ++(0,.25) -- ++(.25,0) node [pos=.5,above] {$\frac{b}{2}$}
			-- ++(0,-.25) node [pos=.5,right] {$\frac{b}{2}$} -- ++(-.25,0);
    	\end{tikzpicture}
	};
    \node [below=.1em of b6] (b7) {
    	\begin{tikzpicture}
    		\draw [fill=gray!70] (0,-.5) -- ++(0,1.25) node [pos=.5,left] {$x+\frac{b}{2}$} 
			-- ++(1.25,0) -- ++(0,-1.25) -- ++(-1.25,0) node [pos=.5,below] {$x+\frac{b}{2}$};
		\draw [dash pattern=on 2pt off 1pt] (0,.5) -- ++(1.25,0)
			(1,-.5) -- ++(0,1.25);
		\node at (1.75,.15) {$=$};
		\node [fill=gray!70,ellipse,minimum width=2em] at (2.4,0.25) {$a$};
		\node at (3,.25) {$+$};
		\draw [fill=gray!70] (3.25,-.125) -- ++(0,.25) -- ++(.25,0) node [pos=.5,above] {$\frac{b}{2}$}
			-- ++(0,-.25) node [pos=.5,right] {$\frac{b}{2}$} -- ++(-.25,0);
    	\end{tikzpicture}
	};
    \node [below=.1em of b7] (b8) {$\left(x+\frac{b}{2}\right)^2=a+\left(\frac{b}{2}\right)^2$};
    \node [below=.1em of b8,draw=red] (b9) {$x=-\frac{b}{2}+\sqrt{a+\frac{b^2}{4}}$};
    \draw [dashed,gray!70] (-2.2,-2.9) -- ++(4.5,0)
    	(-2.2,-5) -- ++(4.5,0)
    	(-2.2,-7.75) -- ++(4.5,0)
    	(-2.2,-10.4) -- ++(4.5,0);
    \draw [->,shorten >= 2pt, shorten <= 2pt] (b31.north west) parabola (b41.north east);
    \draw [->,shorten >= 2pt, shorten <= 2pt] (b31.north east) parabola (b42.north east);
    \draw [->,shorten >= 1pt, shorten <= 2pt] (b43.north) .. controls +(south west:5mm) and +(north:2mm) .. (b51.south);
    \draw [->,shorten >= -2pt, shorten <= 1pt] (b44.north) .. controls +(south west:7mm) and +(north east:5mm) .. (b52.north east);
  \end{tikzpicture}
\end{document}

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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Date/TimeThumbnailDimensionsUserComment
current07:40, 13 December 2014Thumbnail for version as of 07:40, 13 December 2014170 × 513 (39 KB)Krishnavedala (talk | contribs)final result using "plus-or-minus"
06:58, 30 November 2014Thumbnail for version as of 06:58, 30 November 2014190 × 520 (53 KB)Krishnavedala (talk | contribs){{Information |Description ={{en|1=Geometric derivation of completing the square.}} |Source ={{own}} |Author =Krishnavedala |Date =2014-11-30 |Permission = |other_versions = }} {{validSVG}} {{cot|...

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