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Simplifying -2p2 = 12p + 15 Reorder the terms: -2p2 = 15 + 12p Solving -2p2 = 15 + 12p Solving for variable 'p'. Reorder the terms: -15 + -12p + -2p2 = 15 + 12p + -15 + -12p Reorder the terms: -15 + -12p + -2p2 = 15 + -15 + 12p + -12p Combine like terms: 15 + -15 = 0 -15 + -12p + -2p2 = 0 + 12p + -12p -15 + -12p + -2p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -15 + -12p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 12p + 2p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 12p + 2p2)' equal to zero and attempt to solve: Simplifying 15 + 12p + 2p2 = 0 Solving 15 + 12p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 6p + p2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 6p + -7.5 + p2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 6p + p2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 6p + p2 = 0 + -7.5 6p + p2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 6p + p2 = -7.5 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = -7.5 + 9 Reorder the terms: 9 + 6p + p2 = -7.5 + 9 Combine like terms: -7.5 + 9 = 1.5 9 + 6p + p2 = 1.5 Factor a perfect square on the left side: (p + 3)(p + 3) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (p + 3) equal to 1.224744871 and -1.224744871.Subproblem 1
p + 3 = 1.224744871 Simplifying p + 3 = 1.224744871 Reorder the terms: 3 + p = 1.224744871 Solving 3 + p = 1.224744871 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 1.224744871 + -3 Combine like terms: 3 + -3 = 0 0 + p = 1.224744871 + -3 p = 1.224744871 + -3 Combine like terms: 1.224744871 + -3 = -1.775255129 p = -1.775255129 Simplifying p = -1.775255129Subproblem 2
p + 3 = -1.224744871 Simplifying p + 3 = -1.224744871 Reorder the terms: 3 + p = -1.224744871 Solving 3 + p = -1.224744871 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -1.224744871 + -3 Combine like terms: 3 + -3 = 0 0 + p = -1.224744871 + -3 p = -1.224744871 + -3 Combine like terms: -1.224744871 + -3 = -4.224744871 p = -4.224744871 Simplifying p = -4.224744871Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.775255129, -4.224744871}Solution
p = {-1.775255129, -4.224744871}
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