Solve for x: 84635.5790x + 84635.5790 = 215900.9.

Step-by-step solution

1. 1

   Notice that the same number appears twice. The coefficient of $x$ and the constant on the left are identical, so the left side factors:

   $84635.5790\,(x+1)=215900.9$

   This is worth spotting because it replaces a subtraction and a division with a single division, removing one chance to lose digits.

2. 2

   Divide by the common factor.

   $x+1=\frac{215900.9}{84635.5790}=2.5509473\ldots$

   Carry at least seven significant figures here; the numbers are large and the answer is small, so early rounding hides in exactly the digits you care about.

3. 3

   Subtract 1 to isolate $x$.

   $x=2.5509473-1=1.5509473\approx 1.55095$

4. 4

   Cross-check with the subtract-first route. Subtracting $84635.5790$ from both sides gives

   $84635.5790x=215900.9-84635.5790=131265.321$

   $x=\frac{131265.321}{84635.5790}=1.5509473$

   Both routes agree, which is the point of doing the second one.

5. 5

   Verify by multiplying back. $84635.5790\times 1.5509473=131265.32$, and adding $84635.579$ returns $215900.90$ ✓. As a guard against a slipped digit, note that a wrong value such as $1.55198$ would give $84635.579\times 1.55198=131352.7$ and a left side of $215988.3$ — off by nearly $90$, so back-substitution catches it immediately.