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December 17th, 2015, 09:43 AM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Absolute value term in a quadratic.
Example: x^2 + x  7  9 = 0 Can be solved this way : x^2 + SQRT[(x  7)^2]  9 = 0 SQRT[(x  7)^2] = 9  x^2 squaring both sides and simplifying: x^4  19x^2 + 14x + 32 = 0 Soooo....got rid of absolute term x  7 After googling "quadratic with absolute value term", I saw a few ways to handle these, but not the above. Did I simply "invent something stupid"? 
December 17th, 2015, 10:02 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 
That looks fairly normal to me. I'd consider writing $y=x7$ so that $x^2=y^2+14y+49 = y^2\pm 14y+49 $ and substituting into the original equation allows the use of the quadratic formula to garner solutions. Last edited by v8archie; December 17th, 2015 at 10:48 AM. 
December 17th, 2015, 01:45 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 
You have two possibilities: x^2+x16 (x > 7) or x^2x2 (x < 7). Solve for x in each case and use any solution fitting the condition. Note: I found no solution for the first case and 2 for the second. Last edited by mathman; December 17th, 2015 at 10:45 PM. Reason: correct error 
December 17th, 2015, 02:11 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 
I do think that is probably the easiest approach.

December 17th, 2015, 04:22 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
December 18th, 2015, 02:47 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  
December 18th, 2015, 03:29 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Once more: I simply made up an equation. Purpose was not to solve it, but use it as illustration. Merci. 
December 19th, 2015, 03:08 PM  #8 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  
December 19th, 2015, 04:18 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Agree...but much easier when writing a program...my only purpose. That one was easy to handle, but not all are... 

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