SOLUTION: When the sum of 522 and three times a positive number is subtracted from the square of the number, the result is 126. Find the number.

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Question 831320: When the sum of 522 and three times a positive number is subtracted from the square of the number, the result is 126. Find the number.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Already been asked a few minutes ago. I would start like this translation to symbols.

p%5E2-%28522%2B3p%29=126
Simplify.
p%5E2-522-3p=126
p%5E2-3p-522-126=0
p%5E2-3p-648=0

Examine the constant term.
648=9*72=9*2*36=9*2*6*6=3*3*2*2*2*3*3=2*2*2*3*3*3*3;
Consider 24 and 27 found from the prime factorization.
Try:
highlight%28%28p++%2B24%29%28p+-27%29=0%29 Factorable that way.
Pick highlight%28p=27%29