If I have an equation, say $x^2 + 9x-93=0$, why can't I just take the derivative on both sides to get $2x = -9$ and therefore $x = -\dfrac{9}{2}$. What is the reason behind why what I did is wrong?
Let's say we have $x^2=25$ So we have two real roots ie $+5$ and $-5$.  But if we were to differentiate on both sides with respect to $x$ we'll have the equation $2x=0$ which gives us the only root as $x=0$.  So does differentiating on both sides of an equation alter it? If it does, then how do we conveniently do it in Integration by substitutions? If not then what exactly is going on here ?
In QGIS (1.8.0-Lisboa) on Windows (OSGeo4W Install), how would you resize a feature proportionally?  The only way I've found to do this is by hand using either the Freehand Editing (0.2.6) plugin or the Reshape Features button. Neither of these provides a means to uniformly scale (as in resize) the selected feature up or down.  For example, I want to increase the features size by 130% so that you retain the shape of the feature but expand the area of the shape itself proportionally in all directions. Let $m$ and $n$ be two integers. Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.   I think I have to use the contrapositive to solve this. So I assume $\neg P\implies Q$ and I have to derive $\neg Q$? I know its easier to show odd numbers rather than even... but im still unsure how to do this practice problem. Decode Base64 data in Java I have an image that is Base64 encoded. What is the best way to decode that in Java? Hopefully using only the libraries included with Sun Java 6. After running a VM and logging out, I got a black screen. I powered off and re-started but got the same after the bios option in start up passed. Several attempts went bye with the same result. So I fiddled with bios boot options a bit and was able to get to a different looking Ubuntu start up screen which, after entering pass key would run a series of commands that were too numerous and frantic to make out. They appeared to be overlapped/layered (the text that is) and seemingly repeating endlessly. I had to power down to get it to stop and re-booting just had the same effect. Finally, I hit the down arrow key when prompted for "disk sda5_crypt" at the pseudo Ubuntu log-in screen I mentioned before. This brought me to an all black screen which read something like:  lvmetad not active cannot process volume group "umbuntu-vg" unlock disk sda5_crypt**   From here I entered a password and Ubuntu start up ran.  That was an unsettling hour or so and I'd like to avoid that in the future. Any ideas what caused it and how to avoid it going forward?  Should have said this before but Ubuntu is the only OS on my machine and my optical drive cannot be opened manually. MacBook [Pro] - how many displays, what resolution/frequency? How do I find out the number, type, resolution &amp; refresh rate of additional monitors I can attach to my MacBook or MacBook Pro?  This is an attempt at a canonical QA, as per the Meta QA -   to try prevent the myriad "same but different" questions we get on every possible combination of computers, cable &amp; monitors There are perfectly good resources out there that Ask Different should not have to duplicate the efforts of. How do I close a tkinter window? How do I end a Tkinter program? Let's say I have this code:  from Tkinter import *  def quit():     # code to exit  root = Tk() Button(root, text="Quit", command=quit).pack() root.mainloop()   How should I define the quit function to exit my application? Renormalized mass I am reading Schwarz QFT and I reached the mass renormalization part. So he introduces, after renormalization, a physical mass, defined as the pole of the renormalized propagator, and a renormalized mass which can be the physical mass, but can also take other values, depending on the subtraction schemes used. Are these masses, other than the physical one, observable in any way experimentally, or are they just ways to do the math easier (using minimal subtraction instead of on-shell scheme, for example)?   Also, in the case of charge renormalization, the explanation was that due to the vacuum polarization, the closer you are to the charge, the more you see of it, so the charge of the particle increases with the momentum you are testing the particle with. However, I am not sure I understand, from a physical point of view, why do you need to renormalize the mass. Is this physical mass (defined as the pole of the renormalized propagator) the same no matter how close you get, or it also changes with energy? And if it changes, what is shielding it at big distances? What's the standard "roadmap" to learning quantum physics? What methods can I use to infer a distribution if I know only three percentiles?  For example, I know that in a certain data set, the fifth percentile is 8,135, the 50th percentile is 11,259, and the 95th percentile is 23,611.  I want to be able to go from any other number to its percentile.  It's not  my data, and those are all the statistics I have.  It's clear that the distribution isn't normal.  The only other information I have is that this data represents government per-capita funding for different school districts.  I know enough about statistics to know that this problem has no definite solution, but not enough to know how to go about finding good guesses.  Would a lognormal distribution be appropriate?  What tools can I use to perform the regression (or do I need to do it myself)? Check if table exists in SQL Server I would like this to be the ultimate discussion on how to check if a table exists in SQL Server 2000/2005 using SQL Statements.  When you Google for the answer, you get so many different answers. Is there an official/backward and forward compatible way of doing it?  Here are two possible ways of doing it. Which one among the two is the standard/best way of doing it?  First way:  IF EXISTS (SELECT 1             FROM INFORMATION_SCHEMA.TABLES             WHERE TABLE_TYPE='BASE TABLE'             AND TABLE_NAME='mytablename')     SELECT 1 AS res ELSE SELECT 0 AS res;   Second way:  IF OBJECT_ID (N'mytablename', N'U') IS NOT NULL     SELECT 1 AS res ELSE SELECT 0 AS res;   MySQL provides the simple   SHOW TABLES LIKE '%tablename%';    statement. I am looking for something similar. I know that the compiler will sometimes initialize memory with certain patterns such as 0xCD and 0xDD.  What I want to know is when and why this happens.  When  Is this specific to the compiler used?  Do malloc/new and free/delete work in the same way with regard to this?  Is it platform specific?  Will it occur on other operating systems, such as Linux or VxWorks?  Why  My understanding is this only occurs in Win32 debug configuration, and it is used to detect memory overruns and to help the compiler catch exceptions.  Can you give any practical examples as to how this initialization is useful?  I remember reading something (maybe in Code Complete 2) saying that it is good to initialize memory to a known pattern when allocating it, and certain patterns will trigger interrupts in Win32 which will result in exceptions showing in the debugger.  How portable is this? Is there a way to view your own progress towards certain badges? For example:   Tumbleweed - What value constitutes low views for a week? Fanatic  – Is there a way to view how many days in a row you currently have? Beta – Is it even possible to get this badge anymore? Formation of ammonia from air and moisture On extended bicycle trips I sometimes slept under a plastic sheet, which helped with mosquitoes on hot nights. But there was a noticeable build-up of ammonia which made this almost impossible for more than an hour or so at a time.   Air is mostly nitrogen $(N_2)$ and there is always water (containing hydrogen) on a humid day. But I wonder about the mechanism for the formation of ammonia under these circumstances? There are (according to Wiki) trace amounts of methane and $H_2$ in the air. But methane and hydrogen (g) are I think pretty stable.   I wonder if the presence of exhaled air (containing $CO_2)$ could be a factor?  Thanks for any ideas. How to split strings into text and number? I'd like to split strings like these  'foofo21' 'bar432' 'foobar12345'   into  ['foofo', '21'] ['bar', '432'] ['foobar', '12345']   Does somebody know an easy and simple way to do this in python? The link button in the post editor incorrectly escapes square brackets in inline code.  To reproduce:   Write the following MarkDown in the editor  text text `function[]` text text  Select `function[]`, press the link button (), and enter some link the result will be [`function\[\]`][1] which renders as function\[\]   This comes up very often in   when I'm linking to the documentation because the usual way to indicate that a symbol is a function in Mathematica is adding [] after it.  This is a minor thing, as it's easy to manually remove the backslashes, but it's somewhat annoying so I thought I'd mention it.    Edit by Mr.Wizard It is September 2013 and this still hasn't been fixed.  While "adding [] after it" is not presently the custom on Mathematica.SE this is still a bug and still needs to be fixed. Calculate the factorial of an arbitrarily large number, showing all the digits Standard nomenclature for component types What prefixes should be used on reference designators for components of various types?  I think we can all agree that "R##" refers to a resistor, "C##" refers to a capacitor, and "L##" refers to an inductor.  Beyond that, it appears to be a mishmash of conventions.    I've seen both "IC" and "U" used for chips.   "Q", "T", and "M" have been used for transistors and MOSFETs.  Ordinarily, "D##" is used for diodes, but LEDs and Zeners get special treatment on some boards.    What standards are available for reference, and who endorses them?  JEDEC, ISO, IEEE, and other standardization bodies are welcome references (though I'd prefer an inexpensive standard), but I'm also curious to see what's used at various companies other than my own.    Edit:  What I'd really like to see is a list in an answer here which complies with the standard (even if it's just a quote). Create SOAP envelope of XML and send it as HttpWebRequest to WebService Webform redirect I'd like to do something pretty straightforward: After user fills out a , I'd like a button that simply redirects them to a URL (in this case it's to a demo sandbox). Of course I'd want the user to fill in their info to capture for lead-generation purposes. My  is set up correctly in that it correctly captures all the user fields and submits them to me via email. However, upon completion "click" I'd like to have the user redirected to a determined internal URL www.mysite.com/foo  I can't figure out how this is done with the vanilla webform settings. Am I missing something obvious? How do I create a new object using Python in Blender 2.80? As part of an existing add-on, I'm trying to create an object and add it to the scene using Python. I followed a Blender Cookbook tutorial found here: . I use the following code to do so:  emptyMesh = bpy.data.meshes.new('emptyMesh') theObj = bpy.data.objects.new("object_name", emptyMesh) bpy.context.scene.objects.link(theObj)   But I get the following error when I try to link theObj to the scene objects:  AttributeError: 'bpy_prop_collection' object has no attribute 'link'   This works just fine in Blender 2.76-2.79, but doesn't work in the 2.80 test build I downloaded. Was there a change to the Python API? Or is this maybe a bug in the test build?