SOLUTION: The sum of a number and 21 times it's reciprocal is -10. Find the number?

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Question 517039: The sum of a number and 21 times it's reciprocal is -10. Find the number?
Found 3 solutions by mananth, josmiceli, richwmiller:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the number

x+21/x = -21
LCD = x
multiply by LCD
x^2+21=-21x
x^2+21x+21=0
Find the roots of the equation by quadratic formula

a= 1 ,b= 21 c 21

b^2-4ac= 441 - -84
b^2-4ac= 357
sqrt%28%09357%09%29= 18.89
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -21 + 18.89 )/ 2
x1= -1.05
x2=( -21 -18.89 ) / 2
x2= -19.947
m.ananth@hotmail.ca



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+n+%2B+21%2A%281%2Fn%29+=+-10+
Multiply both sides by n
+n%5E2+%2B+21+=+-10n+
+n%5E2+%2B+10n+=+-21+
Complete the square
+n%5E2+%2B+10n+%2B+%2810%2F2%29%5E2+=+-21+%2B+%2810%2F2%29%5E2+
+n%5E2+%2B+10n+%2B+25+=+-21+%2B+25+
+%28+n+%2B+5+%29%5E2+=+4+
Take the square root of both sides
+n+%2B+5+=+2+
+n+=+-3+
and also
+n+%2B+5+=+-2+
+n+=+-7+
check answers:
+n+%2B+21%2A%281%2Fn%29+=+-10+
+-3+%2B+21%2A%281%2F%28-3%29%29+=+-10+
+-3+-+7+=+-10+
+-10+=+-10+
OK
+-7+%2B+21%2A%281%2F%28-7%29%29+=+-10+
+-7+-+3+=+-10+
+-10+=+-10+

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x+21/x=-10
x^2+21+10x=0
x^2+10x+21=0
(x+7)*(x+3)=0
x=-7
x=-3
check -3
-3+21/-3=-10
-3-7=-10
-10=-10
ok
check -7
-7+21/-7=-10
-7-3=-10
-10=-10
ok