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Simplifying -2p2 + 16p + 20 = 0 Reorder the terms: 20 + 16p + -2p2 = 0 Solving 20 + 16p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 8p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 8p + -1p2)' equal to zero and attempt to solve: Simplifying 10 + 8p + -1p2 = 0 Solving 10 + 8p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -8p + p2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -8p + 10 + p2 = 0 + 10 Reorder the terms: -10 + 10 + -8p + p2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8p + p2 = 0 + 10 -8p + p2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8p + p2 = 10 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 10 + 16 Reorder the terms: 16 + -8p + p2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8p + p2 = 26 Factor a perfect square on the left side: (p + -4)(p + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (p + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
p + -4 = 5.099019514 Simplifying p + -4 = 5.099019514 Reorder the terms: -4 + p = 5.099019514 Solving -4 + p = 5.099019514 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + p = 5.099019514 + 4 p = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 p = 9.099019514 Simplifying p = 9.099019514Subproblem 2
p + -4 = -5.099019514 Simplifying p + -4 = -5.099019514 Reorder the terms: -4 + p = -5.099019514 Solving -4 + p = -5.099019514 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + p = -5.099019514 + 4 p = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 p = -1.099019514 Simplifying p = -1.099019514Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.099019514, -1.099019514}Solution
p = {9.099019514, -1.099019514}
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