Solve (x + 1) x 1.76566975 = 25.

Step-by-step solution

1. 1

   Treat (x + 1) as a single unknown. The whole bracket is multiplied by one constant, so there is no need to distribute. Let $u = x+1$; then $1.76566975\,u = 25$.

2. 2

   Divide by the multiplier. $u = x+1 = \frac{25}{1.76566975}.$ Undoing a multiplication with a division is the only inverse step needed at this stage.

3. 3

   Evaluate the quotient exactly. Writing $1.76566975 = \tfrac{7062679}{4000000}$ turns the division into $\frac{25 \cdot 4000000}{7062679} = \frac{100000000}{7062679} = 14.15893318\ldots$ Note the eighth digit: a decimal division truncated too early gives $14.1589364$, which is wrong from the seventh significant figure onward.

4. 4

   Subtract 1 to recover x. $x = \frac{100000000}{7062679} - 1 = \frac{92937321}{7062679} \approx 13.15893318.$

5. 5

   Verify by multiplying back. $(13.15893318+1) \cdot 1.76566975 = 14.15893318 \cdot 1.76566975 = 25.0000000$, so the answer closes to eight decimals.

6. 6

   Note where the multiplier came from. $1.76566975 = 0.79 \cdot 1.15 \cdot 1.3 \cdot 1.3 \cdot 1.15$ exactly, so this equation is the 'solve' companion to collapsing that chain of five percentage factors.