The first step is to expand the equation using the FOIL method, which stands for First, Outer, Inner, and Last. This means multiplying the first terms, outer terms, inner terms, and last terms of the binomials.
To isolate the variable, you will need to use the inverse operations of addition and multiplication. First, distribute the p to the terms inside the parentheses. Then, subtract the constant term on the right side from both sides. Finally, take the square root of both sides to isolate the variable.
In this case, you will need to combine the constant terms on one side of the equation. For example, if there is a constant term of 5 on both sides, you can subtract 5 from both sides to eliminate it. Then, follow the steps for isolating the variable as normal.
To check if your solution is correct, you can substitute the values of the variables into the original equation and see if it satisfies the equation. For example, if your solution is y = 3 and x = 2, you would substitute those values into the equation to see if (3 - a)^2 = p(2 - e) is true.
Yes, there are a few special cases to consider. First, if p = 0, the equation becomes (y - a)^2 = 0, and the only solution is y = a. Second, if y = a and x = e, the equation becomes 0 = 0, and there are infinitely many solutions. Lastly, if p < 0, there are no real solutions to the equation.