For example, say I wanted to find a perfect square of the form
z^2 + 180z - 88

The solutions manual shows the answer is z = 22, but how do I figure out this kind of problem in general?

I am not looking for a zero of the quadratic. I'm looking for an integer generated by this quadratic form that is a perfect square.
asked Mar 6, 2011 in Algebra 1 Answers by anonymous
Try completing the square?
pink chicken that wont help this person

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11 Answers

assuming z^2+180-88=m^2

rewrite it in a form of z(z+180) = m^2 + 88

since LHS is a form of 2 factors z and z+180, the right handside must be also in such a form as a x b therefore m must have same factors as 88, you can start from there and try the factors of 88
answered Mar 7, 2011 by HenryYang Level 3 User (2,140 points)

 27+12+6=45   15+9+21=45                                                                   3+18+24=45



answered Jun 14, 2012 by anonymous
2,6,10,................................................................,142  is an AP

using this ap make magic square
answered Aug 14, 2012 by anonymous
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answered Sep 24, 2012 by anonymous
29   16   91   77   62                                                                 71   67   22   19   96                                                                 12   99   76   61   27                                                                  66  21   17   92   79                                                                  97  72   69   26   11                                               This is a reversable magic square of 5,  I'll explain the reversable part some time in this or its following parah.  As you see that the Nos. I've chosen are 11-12-16-17-19; 21-22-26-27- 29; 61-62-66-67-68-69; 71-72-76-77-79; 91-92-96-97-98-99, all these 25 numbers are not repeated in the solution of the square at the start, if you add them horizontally, vertically, diagonally, a pattern form: 29-62-97-11-76 which also total to the same as in horizontals etc.; add in another pattern: 91-12-69-27-76.  These two patterns can be done in another way i.e., add 29-91-12-76-67; shift to the 2nd vertical line, repeat the same pattern by adding the Nos. 16-77-99-61-22; shift in the same manner in the 3rd, 4th and 5th iine, you'll get the same total (275).  Now shift to the 2nd row i.e., add 71-22-66-17-99.  Go to the 2nd, 3rd, 4th and 5th line with the same pattern, getting the same total when added.  Come down to the 3rd tine and do as done in the previous 2 lines, simialrly, come down to the 4th line, repeat as done earlier and then to the 5th line likewise, total in all these 25 similar patterns would give you the total of 275.  Now change the pattern i.e., add 16-71-99-22-67; go to the 2nd, 3rd, 4th and 5th line, getting the same total in each way.  Go to the 2nd line, 3rd, 4th and 5th line, adding in the form of this 2nd pattern.  You can go to a 3rd pattern i.e., add 29-16-71-67-92, shift to the vertical line to the right keeping the same pattern i.e., 16-91-67-22-79; 91-77-22d-19-66; 77- 62-19-96-79; 62-96-29-71-17.  As done in the previous patterns, continue doing likewise, getting another 25 solutions that again give you the total of 275.  Change to another pattern: add 71- 99-17-26-62; 12-21-69-77-96; 66-72-91-19-27; 97-16-22-61-79; keep the same pattern and add72-17-61-96-29, 69-92-27-71-16; 26-79-12-67-91; 11-66-99-22-77, getting the same total  of 275.  I'm falling short of time, look carefully, you'll come out with several other patterns like: 71-22-96-17- 69.  Continue the same way as you've read and totalled the earlier patterns so to get another 25 solutions.  This is just one form in which you'll be able to trace hundreds of patterns, may be more, but when we meet next, I'll be giving you a very difficult pattern of 5.  As in the beginning I told you that this is a reversable magic square of 5 which you cannot do by typing, take a pen and a paper and practice for a minute or so, how to write 2 in such a way that when reversed, it reads as 7.  When you've succeeded in doing so, take this example: Write the 1st horizontal lines numbers by the use of a pen.  As the numbers in the 3rd horizontal line are: 12-99-76-61-27 which total to 275, when you reverse the square, you'll read these very numbers as 27-19-92- 66-71 and go through the square as a whole, the 25 numbers I used in this square of 5, will remain the same but produce a different answer altogether.  There's just one more type of reversable square of 7, see if you succeed.
answered Feb 9, 2013 by Jatinder Ahooja (140 points)
how to answer perfectsquare
answered Jun 4, 2013 by anonymous
answered Mar 17, 2014 by anonymous

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answered Jun 5, 2014 by yoyp
( e + 2a + q ) =
answered Jun 22, 2014 by anonymous
  1. (a+b2) = (a+b) (a+b)
              = a2+ab+ba+b2
              = a2+2ab+b2

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answered Jun 25, 2014 by Vanessa

Try working with the factors of 88.


z(z+180) = m^2 + 88



The factors of 88

Answer : 1,2,4,8,11,22,44,88,

answered 6 days ago by Dino Zammit Level 3 User (2,620 points)
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