How do you solve x=\frac{5}{2}\times (1,8\times 10^{23})\times (x-330)?

Oct 31, 2017

The short answer is $x = 330$

Explanation:

x=5/2×(1.8×10^23)xx(x−330)

1)You can start to the simple calculation:

x=4.5×10^23xx(x−330)

2)4.5×10^23 is a huge number, let's replace it by A:

x=A(x−330)

3) Isolating the $x$s:

$\left(1 - A\right) x = - 330 A$

$x = 330 \left(\frac{- A}{1 - A}\right)$

4)$A$ is so big that $\left(\frac{- A}{1 - A}\right)$ is infinitesimally equal to 1, therefore,

$x = 330$

5)Nevertheless, let's try to calculate the "right answer"

$\left(\frac{- A}{1 - A}\right) = \frac{A}{A - 1} = \frac{A - 1}{A - 1} + \frac{1}{A - 1} \approx 1 + \frac{1}{A} = 1 + \frac{1}{4.5 \times {10}^{23}} =$

$1 + \left(\frac{2}{9}\right) \times {10}^{-} 23$

No computer can handle with 23 digits numbers. so we have to continue like this:

$x = 330 \left(\frac{- A}{1 - A}\right) \approx 330 \left(1 + \left(\frac{2}{9}\right) \times {10}^{-} 23\right)$

$x = 330 + 330 \times \left(\frac{2}{9}\right) \times {10}^{-} 23$=330+73.333xx10^-23#

Now we get the ridiculous number of :

$330.000000000000000000000733$