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Simplifying -8p3 + 36p2 + 28p = 0 Reorder the terms: 28p + 36p2 + -8p3 = 0 Solving 28p + 36p2 + -8p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4p'. 4p(7 + 9p + -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 '(7 + 9p + -2p2)' equal to zero and attempt to solve: Simplifying 7 + 9p + -2p2 = 0 Solving 7 + 9p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -4.5p + p2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -4.5p + 3.5 + p2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -4.5p + p2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -4.5p + p2 = 0 + 3.5 -4.5p + p2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -4.5p + p2 = 3.5 The p term is -4.5p. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5p + 5.0625 + p2 = 3.5 + 5.0625 Reorder the terms: 5.0625 + -4.5p + p2 = 3.5 + 5.0625 Combine like terms: 3.5 + 5.0625 = 8.5625 5.0625 + -4.5p + p2 = 8.5625 Factor a perfect square on the left side: (p + -2.25)(p + -2.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (p + -2.25) equal to 2.926174978 and -2.926174978.Subproblem 1
p + -2.25 = 2.926174978 Simplifying p + -2.25 = 2.926174978 Reorder the terms: -2.25 + p = 2.926174978 Solving -2.25 + p = 2.926174978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = 2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = 2.926174978 + 2.25 p = 2.926174978 + 2.25 Combine like terms: 2.926174978 + 2.25 = 5.176174978 p = 5.176174978 Simplifying p = 5.176174978Subproblem 2
p + -2.25 = -2.926174978 Simplifying p + -2.25 = -2.926174978 Reorder the terms: -2.25 + p = -2.926174978 Solving -2.25 + p = -2.926174978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = -2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = -2.926174978 + 2.25 p = -2.926174978 + 2.25 Combine like terms: -2.926174978 + 2.25 = -0.676174978 p = -0.676174978 Simplifying p = -0.676174978Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.176174978, -0.676174978}Solution
p = {0, 5.176174978, -0.676174978}
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