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Simplifying 8p3 + -20p2 + -24p = 0 Reorder the terms: -24p + -20p2 + 8p3 = 0 Solving -24p + -20p2 + 8p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4p'. 4p(-6 + -5p + 2p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-6 + -5p + 2p2)' equal to zero and attempt to solve: Simplifying -6 + -5p + 2p2 = 0 Solving -6 + -5p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -2.5p + p2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5p + p2 = 0 + 3 -2.5p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5p + p2 = 3 The p term is -2.5p. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5p + 1.5625 + p2 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5p + p2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5p + p2 = 4.5625 Factor a perfect square on the left side: (p + -1.25)(p + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (p + -1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
p + -1.25 = 2.136000936 Simplifying p + -1.25 = 2.136000936 Reorder the terms: -1.25 + p = 2.136000936 Solving -1.25 + p = 2.136000936 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = 2.136000936 + 1.25 p = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 p = 3.386000936 Simplifying p = 3.386000936Subproblem 2
p + -1.25 = -2.136000936 Simplifying p + -1.25 = -2.136000936 Reorder the terms: -1.25 + p = -2.136000936 Solving -1.25 + p = -2.136000936 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = -2.136000936 + 1.25 p = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 p = -0.886000936 Simplifying p = -0.886000936Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.386000936, -0.886000936}Solution
p = {0, 3.386000936, -0.886000936}
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