To solve for p, we can begin by isolating the variable on one side of the equation. Here are the steps to do that:
1. Distribute the 82.78 to both terms inside the parentheses:
82.78p + 82.78 * 11.892 = 72.8464
2. Simplify the equation further:
82.78p + 981.90336 = 72.8464
3. Next, we want to get rid of the constant term (981.90336) by subtracting it from both sides of the equation:
82.78p = 72.8464 - 981.90336
4. Calculate the value on the right-hand side of the equation:
82.78p = -909.05696
5. Finally, to solve for p, divide both sides of the equation by the coefficient of p, which is 82.78:
p = (-909.05696) / 82.78
Therefore, the solution for p is approximately -10.9701 when rounded to four decimal places. However, the instructions state not to round the answer, so the exact value is p = -909.05696 / 82.78.