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Simplifying 2p4 + 4p2 + -250 = 0 Reorder the terms: -250 + 4p2 + 2p4 = 0 Solving -250 + 4p2 + 2p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-125 + 2p2 + p4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + 2p2 + p4)' equal to zero and attempt to solve: Simplifying -125 + 2p2 + p4 = 0 Solving -125 + 2p2 + p4 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 2p2 + 125 + p4 = 0 + 125 Reorder the terms: -125 + 125 + 2p2 + p4 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 2p2 + p4 = 0 + 125 2p2 + p4 = 0 + 125 Combine like terms: 0 + 125 = 125 2p2 + p4 = 125 The p term is 2p2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p2 + 1 + p4 = 125 + 1 Reorder the terms: 1 + 2p2 + p4 = 125 + 1 Combine like terms: 125 + 1 = 126 1 + 2p2 + p4 = 126 Factor a perfect square on the left side: (p2 + 1)(p2 + 1) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (p2 + 1) equal to 11.22497216 and -11.22497216.Subproblem 1
p2 + 1 = 11.22497216 Simplifying p2 + 1 = 11.22497216 Reorder the terms: 1 + p2 = 11.22497216 Solving 1 + p2 = 11.22497216 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 + p2 = 11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + p2 = 11.22497216 + -1 p2 = 11.22497216 + -1 Combine like terms: 11.22497216 + -1 = 10.22497216 p2 = 10.22497216 Simplifying p2 = 10.22497216 Take the square root of each side: p = {-3.197651038, 3.197651038}Subproblem 2
p2 + 1 = -11.22497216 Simplifying p2 + 1 = -11.22497216 Reorder the terms: 1 + p2 = -11.22497216 Solving 1 + p2 = -11.22497216 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 + p2 = -11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + p2 = -11.22497216 + -1 p2 = -11.22497216 + -1 Combine like terms: -11.22497216 + -1 = -12.22497216 p2 = -12.22497216 Simplifying p2 = -12.22497216 Reorder the terms: 12.22497216 + p2 = -12.22497216 + 12.22497216 Combine like terms: -12.22497216 + 12.22497216 = 0.00000000 12.22497216 + p2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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