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Simplifying p * p + -1p * p * p * p + -1p * p * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p * p p2 + -1p * p * p * p + -1p * p * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p * p p2 + -1p2 * p * p + -1p * p * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p2 * p p2 + -1p3 * p + -1p * p * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p3 * p p2 + -1p4 + -1p * p * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p * p p2 + -1p4 + -1p2 * p + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p2 * p p2 + -1p4 + -1p3 + 2p * 2p * 2p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Reorder the terms for easier multiplication: p2 + -1p4 + -1p3 + 2 * 2 * 2p * p * p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply 2 * 2 p2 + -1p4 + -1p3 + 4 * 2p * p * p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply 4 * 2 p2 + -1p4 + -1p3 + 8p * p * p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p * p p2 + -1p4 + -1p3 + 8p2 * p + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Multiply p2 * p p2 + -1p4 + -1p3 + 8p3 + 4p * 4p * 4p * 4p + -3p * 3p + 3p * 3p = 0 Reorder the terms for easier multiplication: p2 + -1p4 + -1p3 + 8p3 + 4 * 4 * 4 * 4p * p * p * p + -3p * 3p + 3p * 3p = 0 Multiply 4 * 4 p2 + -1p4 + -1p3 + 8p3 + 16 * 4 * 4p * p * p * p + -3p * 3p + 3p * 3p = 0 Multiply 16 * 4 p2 + -1p4 + -1p3 + 8p3 + 64 * 4p * p * p * p + -3p * 3p + 3p * 3p = 0 Multiply 64 * 4 p2 + -1p4 + -1p3 + 8p3 + 256p * p * p * p + -3p * 3p + 3p * 3p = 0 Multiply p * p p2 + -1p4 + -1p3 + 8p3 + 256p2 * p * p + -3p * 3p + 3p * 3p = 0 Multiply p2 * p p2 + -1p4 + -1p3 + 8p3 + 256p3 * p + -3p * 3p + 3p * 3p = 0 Multiply p3 * p p2 + -1p4 + -1p3 + 8p3 + 256p4 + -3p * 3p + 3p * 3p = 0 Reorder the terms for easier multiplication: p2 + -1p4 + -1p3 + 8p3 + 256p4 + -3 * 3p * p + 3p * 3p = 0 Multiply -3 * 3 p2 + -1p4 + -1p3 + 8p3 + 256p4 + -9p * p + 3p * 3p = 0 Multiply p * p p2 + -1p4 + -1p3 + 8p3 + 256p4 + -9p2 + 3p * 3p = 0 Reorder the terms for easier multiplication: p2 + -1p4 + -1p3 + 8p3 + 256p4 + -9p2 + 3 * 3p * p = 0 Multiply 3 * 3 p2 + -1p4 + -1p3 + 8p3 + 256p4 + -9p2 + 9p * p = 0 Multiply p * p p2 + -1p4 + -1p3 + 8p3 + 256p4 + -9p2 + 9p2 = 0 Reorder the terms: p2 + -9p2 + 9p2 + -1p3 + 8p3 + -1p4 + 256p4 = 0 Combine like terms: p2 + -9p2 = -8p2 -8p2 + 9p2 + -1p3 + 8p3 + -1p4 + 256p4 = 0 Combine like terms: -8p2 + 9p2 = 1p2 1p2 + -1p3 + 8p3 + -1p4 + 256p4 = 0 Combine like terms: -1p3 + 8p3 = 7p3 1p2 + 7p3 + -1p4 + 256p4 = 0 Combine like terms: -1p4 + 256p4 = 255p4 1p2 + 7p3 + 255p4 = 0 Solving 1p2 + 7p3 + 255p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(1 + 7p + 255p2) = 0Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(1 + 7p + 255p2)' equal to zero and attempt to solve: Simplifying 1 + 7p + 255p2 = 0 Solving 1 + 7p + 255p2 = 0 Begin completing the square. Divide all terms by 255 the coefficient of the squared term: Divide each side by '255'. 0.003921568627 + 0.02745098039p + p2 = 0 Move the constant term to the right: Add '-0.003921568627' to each side of the equation. 0.003921568627 + 0.02745098039p + -0.003921568627 + p2 = 0 + -0.003921568627 Reorder the terms: 0.003921568627 + -0.003921568627 + 0.02745098039p + p2 = 0 + -0.003921568627 Combine like terms: 0.003921568627 + -0.003921568627 = 0.000000000000 0.000000000000 + 0.02745098039p + p2 = 0 + -0.003921568627 0.02745098039p + p2 = 0 + -0.003921568627 Combine like terms: 0 + -0.003921568627 = -0.003921568627 0.02745098039p + p2 = -0.003921568627 The p term is 0.02745098039p. Take half its coefficient (0.0137254902). Square it (0.0001883890812) and add it to both sides. Add '0.0001883890812' to each side of the equation. 0.02745098039p + 0.0001883890812 + p2 = -0.003921568627 + 0.0001883890812 Reorder the terms: 0.0001883890812 + 0.02745098039p + p2 = -0.003921568627 + 0.0001883890812 Combine like terms: -0.003921568627 + 0.0001883890812 = -0.0037331795458 0.0001883890812 + 0.02745098039p + p2 = -0.0037331795458 Factor a perfect square on the left side: (p + 0.0137254902)(p + 0.0137254902) = -0.0037331795458 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
p = {0}
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