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what type of equation is this?
- Thread starter namendoza
- Start date
D
Deleted member 4993
Guest
x*x/(.1-x) = 4.5e10, how do I calcuate for x?
Its for a water treatment class. Ive forgot what the steps are to solving this.
Any help or advice would be greatly appreciated.
Thanks,
Nathan.
What you have is:
x * x/(A - x) = B (where A = 0.1 & B = 4.5*1010
x2 = AB - Bx
This a quadratic equation - solve it using your favorite method.
x*x/(.1-x) = 4.5e10, how do I calcuate for x?
Its for a water treatment class. Ive forgot what the steps are to solving this.
Any help or advice would be greatly appreciated.
Thanks,
Nathan.
I think your equation is:
\(\displaystyle \dfrac{x^2}{0.1-x}=4.5 \cdot 10^{10}\)
If it is, you can cross multiply and then use the quadratic formula. Do you remember how to do that?
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Okay, I seem to be having a little trouble doing the problem. I did realize the equation i have is 4.5e7, not 4.5e10. I know that doesn't make a difference on actually going about to get a possible solution. Just though Id correct my mistake.
If I cross multiply, I should get x2 = 4,500,000 - 45,000,000x , correct?
is my next step to move all to one side. if so, it should look like x2 + 45,000,000x - 4,500,000 = 0 , correct?
and than I should have A=1 B=45,000,000 and c = -4,500,000 , cant be correct, because i dont get the correct answer for x.
need a little help here, please.
If I cross multiply, I should get x2 = 4,500,000 - 45,000,000x , correct?
is my next step to move all to one side. if so, it should look like x2 + 45,000,000x - 4,500,000 = 0 , correct?
and than I should have A=1 B=45,000,000 and c = -4,500,000 , cant be correct, because i dont get the correct answer for x.
need a little help here, please.
\(\displaystyle \dfrac{x^2}{0.1 - x} = 4.5 * 10^7 = 4.5 * 10,000,000 = 45,000,000 \implies\)Okay, I seem to be having a little trouble doing the problem. I did realize the equation i have is 4.5e7, not 4.5e10. I know that doesn't make a difference on actually going about to get a possible solution. Just though Id correct my mistake.
If I cross multiply, I should get x2 = 4,500,000 - 45,000,000x , correct?
is my next step to move all to one side. if so, it should look like x2 + 45,000,000x - 4,500,000 = 0 , correct?
and than I should have A=1 B=45,000,000 and c = -4,500,000 , cant be correct, because i dont get the correct answer for x.
need a little help here, please.
\(\displaystyle x^2 = 4,500,000 - 45,000,000x \implies x^2 + 45,000,000x - 4,500,000.\)
So a = 1, b = 45,000,000, and c = -4,500,000. All of this is correct.
Now you do not tell us your answer or how you got it or what purports to be the correct answer so how in the world can you expect us to show you what is wrong.
D
Deleted member 4993
Guest
Okay, I seem to be having a little trouble doing the problem. I did realize the equation i have is 4.5e7, not 4.5e10. I know that doesn't make a difference on actually going about to get a possible solution. Just though Id correct my mistake.
If I cross multiply, I should get x2 = 4,500,000 - 45,000,000x , correct?
is my next step to move all to one side. if so, it should look like x2 + 45,000,000x - 4,500,000 = 0 , correct?
and than I should have A=1 B=45,000,000 and c = -4,500,000 , cant be correct, because i dont get the correct answer for x.
need a little help here, please.
What do you get as solution of the equation?
I get (.1 + 1.49012e-09) & -4.50e07
To keep all the digits from getting in the way, I will let \(\displaystyle k=4.5\cdot 10^7\). Then the quadratic equation isOkay, I seem to be having a little trouble doing the problem. I did realize the equation i have is 4.5e7, not 4.5e10. I know that doesn't make a difference on actually going about to get a possible solution. Just though Id correct my mistake.
If I cross multiply, I should get x2 = 4,500,000 - 45,000,000x , correct?
is my next step to move all to one side. if so, it should look like x2 + 45,000,000x - 4,500,000 = 0 , correct?
and than I should have A=1 B=45,000,000 and c = -4,500,000 , cant be correct, because i dont get the correct answer for x.
need a little help here, please.
\(\displaystyle x^2 + kx - k/10 = 0\).
As part of the solution, you need the "discriminant"
\(\displaystyle d = \sqrt{b^2 - 4ac} = \sqrt{k^2 + 4k/10} = k\ \sqrt{1 + 2/(5\ k)}\)
where I have extracted \(\displaystyle k\) from the square root, by dividing each term under the radical by \(\displaystyle k^2\). Now \(\displaystyle k\) is so large that the square root can be replaced by an approximation to first order in \(\displaystyle 1/k\):
\(\displaystyle d \approx k\ \left(1 + 1/(5\ k)\right) = k + \frac15\)
and the solution of the quadratic formula becomes
\(\displaystyle \displaystyle x = -\frac{k}{2}\ \pm\ \dfrac{k+\frac15}{2} \)
Does that give the two solutions you are looking for?
Hmmm. The answer I just derived doesn't agree with this. In fact, when I insert this value in the quadratic, I getI didn't get the correct answer, so i didn't provide it. Sorry for that. But I know the correct answer is x=.00021, I was given the answer, in the example. I'm just not sure how they got it.
\(\displaystyle (0.00021)^2 + (4.5\cdot 10^7)(0.00021) - (4.5\cdot 10^6) = -4490550 \ne 0\)
so something is wrong with your initial interpretation of the question.
EDIT: the given answer is near the square root of 4.5e(-8) ... negative power of 10!!!
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D
Deleted member 4993
Guest
What exactly are you doing there?↑So I started with x*x/(.1-x) = 4.5e7
.00021 * .00021 = .0000000441
.1 - .00021 = .09979
.0000000441/.09979 = 4.419e7
DrPhil said "so something is wrong with your initial interpretation of the question."
Im not sure what I have wrong.
the answer I was given as x =.00021, I was just complete the question using the answer I was given. I just need to know how they got it. When I try to use the formulas provided I don't get the same answer. Im not sure what im doing wrong or missing. I apologize for my lack of understanding.
Im not sure what I have wrong.
the answer I was given as x =.00021, I was just complete the question using the answer I was given. I just need to know how they got it. When I try to use the formulas provided I don't get the same answer. Im not sure what im doing wrong or missing. I apologize for my lack of understanding.
Look. You do not show us what you are doing step by step so we cannot figure out where you are making mistakes.DrPhil said "so something is wrong with your initial interpretation of the question."
Im not sure what I have wrong.
the answer I was given as x =.00021, I was just complete the question using the answer I was given. I just need to know how they got it. When I try to use the formulas provided I don't get the same answer. Im not sure what im doing wrong or missing. I apologize for my lack of understanding.
More importantly, the problem you have given and the correct answer you were given do not agree.
\(\displaystyle \dfrac{0.00021^2}{0.1 - 0.00021} = \dfrac{\left(2.1 * 10^{-4}\right)^2}{0.09979} = \dfrac{4.41 * 10^{-8}}{9.979 * 10^{-2}} \approx 0.442 * 10^{-6} = 4.42 * 10^{-7} \ne 45,000,000.\)
So there are only two possibilities.
One is that you have set up the problem incorrectly.
The other is that the answer you were given is wrong.
What is the original problem EXACTLY.
Okay, I apologize. My version of the question was a copy. And after checking a fellow students hand out, I had 4.5e7 and it was suppose to be 4.5e-7. not sure how the - sign didnt show up. I can now figure it out correctly. Again I apogolize for the wasted time and effort. I really do appreciate the help that was given.
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