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Simplifying (p + 4)(p + -14) = 72 Reorder the terms: (4 + p)(p + -14) = 72 Reorder the terms: (4 + p)(-14 + p) = 72 Multiply (4 + p) * (-14 + p) (4(-14 + p) + p(-14 + p)) = 72 ((-14 * 4 + p * 4) + p(-14 + p)) = 72 ((-56 + 4p) + p(-14 + p)) = 72 (-56 + 4p + (-14 * p + p * p)) = 72 (-56 + 4p + (-14p + p2)) = 72 Combine like terms: 4p + -14p = -10p (-56 + -10p + p2) = 72 Solving -56 + -10p + p2 = 72 Solving for variable 'p'. Reorder the terms: -56 + -72 + -10p + p2 = 72 + -72 Combine like terms: -56 + -72 = -128 -128 + -10p + p2 = 72 + -72 Combine like terms: 72 + -72 = 0 -128 + -10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + -10p + 128 + p2 = 0 + 128 Reorder the terms: -128 + 128 + -10p + p2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -10p + p2 = 0 + 128 -10p + p2 = 0 + 128 Combine like terms: 0 + 128 = 128 -10p + p2 = 128 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 128 + 25 Reorder the terms: 25 + -10p + p2 = 128 + 25 Combine like terms: 128 + 25 = 153 25 + -10p + p2 = 153 Factor a perfect square on the left side: (p + -5)(p + -5) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (p + -5) equal to 12.369316877 and -12.369316877.Subproblem 1
p + -5 = 12.369316877 Simplifying p + -5 = 12.369316877 Reorder the terms: -5 + p = 12.369316877 Solving -5 + p = 12.369316877 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 12.369316877 + 5 Combine like terms: -5 + 5 = 0 0 + p = 12.369316877 + 5 p = 12.369316877 + 5 Combine like terms: 12.369316877 + 5 = 17.369316877 p = 17.369316877 Simplifying p = 17.369316877Subproblem 2
p + -5 = -12.369316877 Simplifying p + -5 = -12.369316877 Reorder the terms: -5 + p = -12.369316877 Solving -5 + p = -12.369316877 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -12.369316877 + 5 Combine like terms: -5 + 5 = 0 0 + p = -12.369316877 + 5 p = -12.369316877 + 5 Combine like terms: -12.369316877 + 5 = -7.369316877 p = -7.369316877 Simplifying p = -7.369316877Solution
The solution to the problem is based on the solutions from the subproblems. p = {17.369316877, -7.369316877}
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