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

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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(22740) About Me  (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".
:
%28-x%29%2F12 = 3*1%2Fx - 1
-x%2F12 = 3%2Fx - 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
%28-6%29%2F12 = 3*1%2F6 - 1
-1%2F2 = 1%2F2 - 1

Answer by KnightOwlTutor(293) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B36+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-12%29%5E2-4%2A1%2A36=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-12%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-12x%2B36+=+%28x-6%29%2A%28x-6%29

Again, the answer is: 6, 6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B36+%29


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