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Simplifying 2p3 + 5p = 3p2 Reorder the terms: 5p + 2p3 = 3p2 Solving 5p + 2p3 = 3p2 Solving for variable 'p'. Reorder the terms: 5p + -3p2 + 2p3 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 5p + -3p2 + 2p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(5 + -3p + 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 '(5 + -3p + 2p2)' equal to zero and attempt to solve: Simplifying 5 + -3p + 2p2 = 0 Solving 5 + -3p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1.5p + p2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5p + -2.5 + p2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5p + p2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5p + p2 = 0 + -2.5 -1.5p + p2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5p + p2 = -2.5 The p term is -1.5p. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5p + 0.5625 + p2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5p + p2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5p + p2 = -1.9375 Factor a perfect square on the left side: (p + -0.75)(p + -0.75) = -1.9375 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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