what is the solution of 82.78 ( p + 11.892) = 72.8464 when solving for p?

Answer 1

To solve the equation \( 82.78 ( p + 11.892) = 72.8464 \) for \( p \), follow these steps:

1. Distribute \( 82.78 \) on the left side of the equation:

   \[ 82.78p + 82.78 \times 11.892 = 72.8464 \]

   First, calculate \( 82.78 \times 11.892 \):

   \[ 82.78 \times 11.892 \approx 985.479536 \]

   So, the equation becomes:

   \[ 82.78p + 985.479536 = 72.8464 \]

2. Isolate \( 82.78p \) by subtracting \( 985.479536 \) from both sides:

   \[ 82.78p = 72.8464 - 985.479536 \]

   Now, calculate \( 72.8464 - 985.479536 \):

   \[ 72.8464 - 985.479536 \approx -912.633136 \]

   Thus, the equation now is:

   \[ 82.78p = -912.633136 \]

3. Solve for \( p \) by dividing both sides by \( 82.78 \):

   \[ p = \frac{-912.633136}{82.78} \]

   Now, calculate \( \frac{-912.633136}{82.78} \):

   \[ p \approx -11.024 \]

Therefore, the solution for \( p \) is approximately:

\[ \boxed{-11.024} \]