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Simplifying (2p + 11)(2p + -13) = 200 Reorder the terms: (11 + 2p)(2p + -13) = 200 Reorder the terms: (11 + 2p)(-13 + 2p) = 200 Multiply (11 + 2p) * (-13 + 2p) (11(-13 + 2p) + 2p * (-13 + 2p)) = 200 ((-13 * 11 + 2p * 11) + 2p * (-13 + 2p)) = 200 ((-143 + 22p) + 2p * (-13 + 2p)) = 200 (-143 + 22p + (-13 * 2p + 2p * 2p)) = 200 (-143 + 22p + (-26p + 4p2)) = 200 Combine like terms: 22p + -26p = -4p (-143 + -4p + 4p2) = 200 Solving -143 + -4p + 4p2 = 200 Solving for variable 'p'. Reorder the terms: -143 + -200 + -4p + 4p2 = 200 + -200 Combine like terms: -143 + -200 = -343 -343 + -4p + 4p2 = 200 + -200 Combine like terms: 200 + -200 = 0 -343 + -4p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -85.75 + -1p + p2 = 0 Move the constant term to the right: Add '85.75' to each side of the equation. -85.75 + -1p + 85.75 + p2 = 0 + 85.75 Reorder the terms: -85.75 + 85.75 + -1p + p2 = 0 + 85.75 Combine like terms: -85.75 + 85.75 = 0.00 0.00 + -1p + p2 = 0 + 85.75 -1p + p2 = 0 + 85.75 Combine like terms: 0 + 85.75 = 85.75 -1p + p2 = 85.75 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 85.75 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 85.75 + 0.25 Combine like terms: 85.75 + 0.25 = 86 0.25 + -1p + p2 = 86 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (p + -0.5) equal to 9.273618495 and -9.273618495.Subproblem 1
p + -0.5 = 9.273618495 Simplifying p + -0.5 = 9.273618495 Reorder the terms: -0.5 + p = 9.273618495 Solving -0.5 + p = 9.273618495 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 9.273618495 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 9.273618495 + 0.5 p = 9.273618495 + 0.5 Combine like terms: 9.273618495 + 0.5 = 9.773618495 p = 9.773618495 Simplifying p = 9.773618495Subproblem 2
p + -0.5 = -9.273618495 Simplifying p + -0.5 = -9.273618495 Reorder the terms: -0.5 + p = -9.273618495 Solving -0.5 + p = -9.273618495 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -9.273618495 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -9.273618495 + 0.5 p = -9.273618495 + 0.5 Combine like terms: -9.273618495 + 0.5 = -8.773618495 p = -8.773618495 Simplifying p = -8.773618495Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.773618495, -8.773618495}
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