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Simplifying 6p2 + 12p + -80 = 0 Reorder the terms: -80 + 12p + 6p2 = 0 Solving -80 + 12p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 6p + 3p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 6p + 3p2)' equal to zero and attempt to solve: Simplifying -40 + 6p + 3p2 = 0 Solving -40 + 6p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + 2p + p2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + 2p + 13.33333333 + p2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + 2p + p2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + 2p + p2 = 0 + 13.33333333 2p + p2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 2p + p2 = 13.33333333 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 13.33333333 + 1 Reorder the terms: 1 + 2p + p2 = 13.33333333 + 1 Combine like terms: 13.33333333 + 1 = 14.33333333 1 + 2p + p2 = 14.33333333 Factor a perfect square on the left side: (p + 1)(p + 1) = 14.33333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (p + 1) equal to 3.785938897 and -3.785938897.Subproblem 1
p + 1 = 3.785938897 Simplifying p + 1 = 3.785938897 Reorder the terms: 1 + p = 3.785938897 Solving 1 + p = 3.785938897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 3.785938897 + -1 Combine like terms: 1 + -1 = 0 0 + p = 3.785938897 + -1 p = 3.785938897 + -1 Combine like terms: 3.785938897 + -1 = 2.785938897 p = 2.785938897 Simplifying p = 2.785938897Subproblem 2
p + 1 = -3.785938897 Simplifying p + 1 = -3.785938897 Reorder the terms: 1 + p = -3.785938897 Solving 1 + p = -3.785938897 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -3.785938897 + -1 Combine like terms: 1 + -1 = 0 0 + p = -3.785938897 + -1 p = -3.785938897 + -1 Combine like terms: -3.785938897 + -1 = -4.785938897 p = -4.785938897 Simplifying p = -4.785938897Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.785938897, -4.785938897}Solution
p = {2.785938897, -4.785938897}
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