# Math Help - Algebra question where the "x" appears twice

1. ## Algebra question where the "x" appears twice

Not sure what this kind of question is called, but here it is:

x10 + (1-x)11 = 10.8

find x.

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I know x = 0.2 but the only way I can find it is with trial and error.\
I have tried shifting terms around but I can not seem to combine the two x's to get a final answer.

If anyone could write out the steps for solving this that would be great
You can rearrange it to: 10x + 11(1-x) = 10.8 if you want, I have written it differently for a specific reason but it is not important for solving the question.
Once again, I can find the answer with trial and error but I don't have time for that in the exam :O

2. Originally Posted by Siddy
Not sure what this kind of question is called, but here it is:

x10 + (1-x)11 = 10.8

find x.

---

I know x = 0.2 but the only way I can find it is with trial and error.\
I have tried shifting terms around but I can not seem to combine the two x's to get a final answer.

If anyone could write out the steps for solving this that would be great
You can rearrange it to: 10x + 11(1-x) = 10.8 if you want, I have written it differently for a specific reason but it is not important for solving the question.
Once again, I can find the answer with trial and error but I don't have time for that in the exam :O

Expand, simplify, solve.

3. x10 + (1-x)11 = 10.8
x10 + 11 -x11 = 10.8
x10 -x11 = 10.8 -11
-x1 = -0.2
x = 0.2

Thanks!

4. I assume that since you have written the numbers AFTER the letters, they are actually the powers, i.e. your equation is

$\displaystyle x^{10} + (1 - x)^{11} = 10.8$

Is this correct?

Edit: I see that it's not. It's convention to usually put the coefficient of x BEFORE the x, then everybody knows that you mean that is a multiple of x and not a power.