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Simplifying 10p + 17p2 + -2p3 = 0 Solving 10p + 17p2 + -2p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(10 + 17p + -2p2) = 0Subproblem 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 '(10 + 17p + -2p2)' equal to zero and attempt to solve: Simplifying 10 + 17p + -2p2 = 0 Solving 10 + 17p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + -8.5p + p2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.5p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -8.5p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.5p + p2 = 0 + 5 -8.5p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.5p + p2 = 5 The p term is -8.5p. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5p + 18.0625 + p2 = 5 + 18.0625 Reorder the terms: 18.0625 + -8.5p + p2 = 5 + 18.0625 Combine like terms: 5 + 18.0625 = 23.0625 18.0625 + -8.5p + p2 = 23.0625 Factor a perfect square on the left side: (p + -4.25)(p + -4.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (p + -4.25) equal to 4.802343178 and -4.802343178.Subproblem 1
p + -4.25 = 4.802343178 Simplifying p + -4.25 = 4.802343178 Reorder the terms: -4.25 + p = 4.802343178 Solving -4.25 + p = 4.802343178 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = 4.802343178 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = 4.802343178 + 4.25 p = 4.802343178 + 4.25 Combine like terms: 4.802343178 + 4.25 = 9.052343178 p = 9.052343178 Simplifying p = 9.052343178Subproblem 2
p + -4.25 = -4.802343178 Simplifying p + -4.25 = -4.802343178 Reorder the terms: -4.25 + p = -4.802343178 Solving -4.25 + p = -4.802343178 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + p = -4.802343178 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + p = -4.802343178 + 4.25 p = -4.802343178 + 4.25 Combine like terms: -4.802343178 + 4.25 = -0.552343178 p = -0.552343178 Simplifying p = -0.552343178Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.052343178, -0.552343178}Solution
p = {0, 9.052343178, -0.552343178}
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