Solve for x: x + x * 0.09 = 1407198.

Step-by-step solution

1. 1

   Understand what the equation models. A quantity $x$ plus $9\%$ of itself totals $1{,}407{,}198$. This is the standard reverse percentage setup: given a gross figure that already includes a $9\%$ add-on (tax, interest, markup), recover the original base.

2. 2

   Factor out x rather than distributing. Both terms on the left share $x$:

   $x(1+0.09)=1407198\qquad\Longrightarrow\qquad 1.09x=1407198$

   The multiplier $1.09$ — not $0.09$ — is the whole point: it is the total after the add-on.

3. 3

   Estimate before dividing. Removing about $9\%$ should shave roughly $\tfrac{1}{12}$ off, so expect something near $1{,}407{,}198-116{,}000\approx1.29$ million. Any answer far from that signals a slipped decimal.

4. 4

   Divide by 1.09.

   $x=\frac{1407198}{1.09}=\frac{140719800}{109}=1{,}291{,}007.33944954\ldots$

   Rounded to cents, $x\approx1{,}291{,}007.34$.

5. 5

   Correct a common miscomputation. A frequently quoted value for this problem is $1{,}291{,}008.2568807339$, but that is wrong: multiplying it back gives $1{,}291{,}008.2569\times1.09=1{,}407{,}199.00$, one whole unit too large. The correct quotient is $1{,}291{,}007.3394495\ldots$

6. 6

   Verify the answer. $1{,}291{,}007.33944954\times1.09=1{,}407{,}198.00000$ ✓. As a cross-check, $9\%$ of $1{,}291{,}007.34$ is $116{,}190.66$, and $1{,}291{,}007.34+116{,}190.66=1{,}407{,}198.00$ ✓.