Solve x + 0.0005 * 52x = 175800 for x.

Step-by-step solution

1. 1

   Multiply the two numerical factors together. The term $0.0005\cdot 52x$ has a numeric coefficient that can be simplified before anything else:

   $0.0005\times 52=0.026$

   so the equation is $x+0.026x=175800$. (In context this is the shape of "principal plus 52 weeks of a $0.05\%$ weekly charge".)

2. 2

   Collect the like terms. The bare $x$ counts as $1x$, so

   $1x+0.026x=1.026x$

   giving $1.026x=175800$. Forgetting the invisible coefficient $1$ here is the single most common error in this type.

3. 3

   Divide by the coefficient.

   $x=\frac{175800}{1.026}$

4. 4

   Clear the decimal to get an exact value. Multiply numerator and denominator by $1000$ and cancel the common factor $6$:

   $x=\frac{175800000}{1026}=\frac{29300000}{171}$

   Since $171=9\times 19$ and $19\nmid 29300000$, this does not reduce further and does not terminate as a decimal: $x=171345.0292397\ldots$

5. 5

   Round appropriately and check. To the cent, $x\approx 171345.03$. Substituting back, $1.026\times\dfrac{29300000}{171}=175800$ exactly, and $171345.02923977+0.026\times 171345.02923977=175800.00$.