Solve for x: -6.75129744499224% = -104,431,740.75 / x * 100%.

Step-by-step solution

1. 1

   Cancel the percent signs on both sides. A percent sign is a factor of $\tfrac{1}{100}$, and here it appears on both sides, so it cancels:

   $-6.75129744499224\%=-0.0675129744499224\quad\text{and}\quad \frac{-104{,}431{,}740.75}{x}\times 100\%=\frac{-104{,}431{,}740.75}{x}$

   so the equation is simply a ratio equation:

   $-0.0675129744499224=\frac{-104{,}431{,}740.75}{x}$

2. 2

   Note the signs match, so the answer is positive. Both sides are negative, and dividing a negative numerator by a positive $x$ keeps it negative. Hence $x>0$ — this is the structure of a percentage loss on a positive base, such as a return of $-6.75\%$ on a portfolio.

3. 3

   Solve for $x$ by cross-multiplying.

   $x=\frac{-104{,}431{,}740.75}{-0.0675129744499224}=\frac{104{,}431{,}740.75}{0.0675129744499224}$

4. 4

   Evaluate the quotient.

   $x\approx 1{,}546{,}839{,}575.67$

   Because the given rate carries $15$ significant figures, the quotient is meaningful to about that precision; rounding the rate to $6.75\%$ first would shift the answer by roughly $200{,}000$.

5. 5

   Check by recomputing the percentage. Dividing back:

   $\frac{-104{,}431{,}740.75}{1{,}546{,}839{,}575.67}=-0.06751297445=-6.751297445\%\;\checkmark$

   A wrong value such as $1{,}546{,}697{,}085$ would instead return $-6.75191\%$, which does not match the given rate — worth checking, because these large quotients are easy to mistype.