SOLUTION: The additive inverse of a number divided by twelve is the same as one less than three times its reciprocal. Find the number

Question 159839: The additive inverse of a number divided by twelve is the same as one less than three times its reciprocal. Find the number
Found 2 solutions by ankor@dixie-net.com, KnightOwlTutor:
Answer by ankor@dixie-net.com(12703) (Show Source):
You can put this solution on YOUR website!
The additive inverse of a number divided by twelve is the same as one less than three times its reciprocal. Find the number
;
Let x = the number
:
The "additive inverse" is just and egg-head's way of saying "negative".
:
= 3* - 1
= - 1
Multiply equation by 12x
x(-x) = 3(12) - 12x
-x^2 = 36 - 12x
0 = x^2 - 12x + 36
Factors to:
(x-6)(x-6) = 0
x = +6 is the number
:
Check solution in original equation
= 3* - 1
= - 1

Answer by KnightOwlTutor(293) (Show Source):
You can put this solution on YOUR website!
X=unknown #
-X= unknown # additive inverse
The equation is
-X/12=3/x-1
Find a common denominator 12X
Multiply each term by 12X
-X^2=3(12)-12x
This is a quadratic equation
add X^2 to both sides and solve

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 6, 6. Here's your graph:

Replace x with 6
-6/12=3/6-1
-1/2=1/2-2/2
-1/2=-1/2