SOLUTION: Hi, I am stuck on this problem and need help... Solve q+5/q = -6 Thanks!

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Question 206050: Hi, I am stuck on this problem and need help...

Solve
q+5/q = -6
Thanks!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
q+5/q = -6
-----------
There are two ways to interpret your problem.
It could be q + (5/q) = -6
or it could be
(q+5)/q = -6
===================
Use parentheses so others can tell which problem
you are dealing with.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation %28q%2B5%29%2Fq=-6 ???


%28q%2B5%29%2Fq=-6 Start with the given equation.


q%2B5=-6q Multiply both sides by 'q'.


q=-6q-5 Subtract 5 from both sides.


q%2B6q=-5 Add 6q to both sides.


7q=-5 Combine like terms on the left side.


q=%28-5%29%2F%287%29 Divide both sides by 7 to isolate q.


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Answer:

So the solution is q=-5%2F7 which approximates to q=-0.714.




OR...Is the equation q%2B5%2Fq=-6 ???


q%2B5%2Fq=-6 Start with the given equation.


q%5E2%2B5=-6q Multiply EVERY term by the LCD 'q' to clear out the fractions.


q%5E2%2B6q%2B5=0 Add 6q to both sides.


Notice that the quadratic q%5E2%2B6q%2B5 is in the form of Aq%5E2%2BBq%2BC where A=1, B=6, and C=5


Let's use the quadratic formula to solve for "q":


q+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


q+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=5


q+=+%28-6+%2B-+sqrt%28+36-4%281%29%285%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


q+=+%28-6+%2B-+sqrt%28+36-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


q+=+%28-6+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Subtract 20 from 36 to get 16


q+=+%28-6+%2B-+sqrt%28+16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


q+=+%28-6+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


q+=+%28-6+%2B+4%29%2F%282%29 or q+=+%28-6+-+4%29%2F%282%29 Break up the expression.


q+=+%28-2%29%2F%282%29 or q+=++%28-10%29%2F%282%29 Combine like terms.


q+=+-1 or q+=+-5 Simplify.


So the solutions are q+=+-1 or q+=+-5