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Simplifying 3p3 + 3p2 + 36p = 0 Reorder the terms: 36p + 3p2 + 3p3 = 0 Solving 36p + 3p2 + 3p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3p'. 3p(12 + p + p2) = 0 Ignore the factor 3.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 '(12 + p + p2)' equal to zero and attempt to solve: Simplifying 12 + p + p2 = 0 Solving 12 + p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + p + -12 + p2 = 0 + -12 Reorder the terms: 12 + -12 + p + p2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + p + p2 = 0 + -12 p + p2 = 0 + -12 Combine like terms: 0 + -12 = -12 p + p2 = -12 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. p + 0.25 + p2 = -12 + 0.25 Reorder the terms: 0.25 + p + p2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + p + p2 = -11.75 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = -11.75 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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