SOLUTION: Find a negative real number such that the square of the sum of the number and 21 is equal to 144 (If there are two correct answers, either answer can be entered.)

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Question 1135200: Find a negative real number such that the square of the sum of the number and 21 is equal to 144
(If there are two correct answers, either answer can be entered.)

Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the negative real number
+%28+n+%2B+21+%29%5E2+=+144+
+n%5E2+%2B+42n+%2B+441+=+144+
+n%5E2+%2B+42n+=+-297+
complete the square
+n%5E2+%2B+42n+%2B+%2842%2F2%29%5E2+=+-297+%2B+%2842%2F2%29%5E2+
+n%5E2+%2B+42n+%2B+441+=+144+ ( what I started with )
+%28+n+%2B+21+%29%5E2+=+12%5E2+
+n+%2B+21+=+12+
+n+=+-9+
and also:
+%28+n+%2B+21+%29%5E2+=+%28-12%29%5E2+
+n+%2B+21+=+-12+
+n+=+-33+
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check the answers:
+%28+n+%2B+21+%29%5E2+=+144+
+%28+-9+%2B+21+%29%5E2+=+12%5E2+
+12%5E2+=+12%5E2+
OK
+%28+-33+%2B+21+%29%5E2+=+12%5E2+
+%28-12%29%5E2+=+12%5E2+
+144+=+144+
OK

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I just solved this problem at this forum couple of days ago under this link

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1135082.html

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1135082.html


            > > > in much simpler way. < < <


For your convenience, I copy and paste here that my solution AGAIN

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%28x%2B21%29%5E2 = 144  ===============> which implies two consequences to be considered:


a)  x+21 = sqrt%28144%29 = 12  ====>  x = 12 - 21 = -9.


b)  x+21 = -sqrt%28144%29 = -12  ====>  x = -12 - 21 = -33.


ANSWER.  The problem has TWO SOLUTIONS. They are the numbers -9 and -33.

Answered and solved.