SOLUTION: the question is the sum of a number and 6 times it's receiprocal is -5. How do I solve this?

Question 37297This question is from textbook Intermediate Algebra
: the question is the sum of a number and 6 times it's receiprocal is -5. How do I solve this? This question is from textbook Intermediate Algebra

Answer by jcmtnez(53) (Show Source): You can put this solution on YOUR website!
Given a number x, the reciprocal of x is 1/x.
6 times the reciprocal of x, is 6/x
and the problem says that the sum of x and its reciprocal is equal to -5,then:
x+6/x=-5 Now we have to eliminate the denominator by multiplying the entire expression by x
x(x)+x(6/x)=x(-5)
x^2+6=-5x
x^2+5x+6=0 Now we have to solve the equation to solve the problem and find the solutions.
The solution is given using the general formula for quadratic equations:

Solutions: x1=-2,x2=-3
We have to solutions and therefore two pair of number for which the stated condition hold.
Those numbers are:
-2 and -1/2 , -3 and -1/3
Proof:
-2+6(-1/2) = -2-3=-5
-3+6(-1/3) = -3-2=-5
Then the solutions are true.
Any doubt?:)

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