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Simplifying -2p(p) + -4(4)(3p + -5) = 0 Multiply p * p -2p2 + -4(4)(3p + -5) = 0 Reorder the terms: -2p2 + -4 * 4(-5 + 3p) = 0 Multiply -4 * 4 -2p2 + -16(-5 + 3p) = 0 -2p2 + (-5 * -16 + 3p * -16) = 0 -2p2 + (80 + -48p) = 0 Reorder the terms: 80 + -48p + -2p2 = 0 Solving 80 + -48p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -24p + -1p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -24p + -1p2)' equal to zero and attempt to solve: Simplifying 40 + -24p + -1p2 = 0 Solving 40 + -24p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 24p + p2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 24p + 40 + p2 = 0 + 40 Reorder the terms: -40 + 40 + 24p + p2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 24p + p2 = 0 + 40 24p + p2 = 0 + 40 Combine like terms: 0 + 40 = 40 24p + p2 = 40 The p term is 24p. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24p + 144 + p2 = 40 + 144 Reorder the terms: 144 + 24p + p2 = 40 + 144 Combine like terms: 40 + 144 = 184 144 + 24p + p2 = 184 Factor a perfect square on the left side: (p + 12)(p + 12) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (p + 12) equal to 13.564659966 and -13.564659966.Subproblem 1
p + 12 = 13.564659966 Simplifying p + 12 = 13.564659966 Reorder the terms: 12 + p = 13.564659966 Solving 12 + p = 13.564659966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = 13.564659966 + -12 Combine like terms: 12 + -12 = 0 0 + p = 13.564659966 + -12 p = 13.564659966 + -12 Combine like terms: 13.564659966 + -12 = 1.564659966 p = 1.564659966 Simplifying p = 1.564659966Subproblem 2
p + 12 = -13.564659966 Simplifying p + 12 = -13.564659966 Reorder the terms: 12 + p = -13.564659966 Solving 12 + p = -13.564659966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = -13.564659966 + -12 Combine like terms: 12 + -12 = 0 0 + p = -13.564659966 + -12 p = -13.564659966 + -12 Combine like terms: -13.564659966 + -12 = -25.564659966 p = -25.564659966 Simplifying p = -25.564659966Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.564659966, -25.564659966}Solution
p = {1.564659966, -25.564659966}
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