3.29x=5.5√(x)+10,000

Question

How in the world do I solve for x without using a calculator? I swear I've been on this for hours. I know the answer is 3133 because I estimated the answer and then began plugging in numbers until I got to the actual answer.

Answer 1

If the question says to solve without a calculator, then admittedly this is a very unreasonable question.

Not even in my olden days, (you know when we had to rely on slide rules and log tables) would they have expected a solution.

I ran it through Wolfram and it shows that you were close,
http://www.wolframalpha.com/input/?i=solve+3.29x%3D5.5%E2%88%9A%28x%29%2B10%2C000

x = appr 3133.1

If you really had to do this .....

3.29x - 10000 = 5.5√x
now square both sides and you would get a quadratic with messy numbers
use the quadratic formula (? with those messy numbers and without a calculator ??) to get two answers.
both must be checked, since we squared our equation.
You would find that the 3133.1 works and the other one does not

Answer 2

It didn't say solve without, I just really wanted to figure out a way to show work and to keep my self esteem intact. I did the squaring on both sides, moved everything to one side and made the other side be 0, and used quadratic equation. Thanks ^.^

Answer 3

Really?
Then what does this mean ?

"How in the world do I solve for x without using a calculator?"

Answer 4

It means I wanted to. I really like math and don't enjoy using calculator. Don't get inquisitorial about it, doesn't really matter.