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Simplifying 36p4 + 14p3 + 35p2 = 0 Reorder the terms: 35p2 + 14p3 + 36p4 = 0 Solving 35p2 + 14p3 + 36p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(35 + 14p + 36p2) = 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 '(35 + 14p + 36p2)' equal to zero and attempt to solve: Simplifying 35 + 14p + 36p2 = 0 Solving 35 + 14p + 36p2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.9722222222 + 0.3888888889p + p2 = 0 Move the constant term to the right: Add '-0.9722222222' to each side of the equation. 0.9722222222 + 0.3888888889p + -0.9722222222 + p2 = 0 + -0.9722222222 Reorder the terms: 0.9722222222 + -0.9722222222 + 0.3888888889p + p2 = 0 + -0.9722222222 Combine like terms: 0.9722222222 + -0.9722222222 = 0.0000000000 0.0000000000 + 0.3888888889p + p2 = 0 + -0.9722222222 0.3888888889p + p2 = 0 + -0.9722222222 Combine like terms: 0 + -0.9722222222 = -0.9722222222 0.3888888889p + p2 = -0.9722222222 The p term is 0.3888888889p. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889p + 0.03780864200 + p2 = -0.9722222222 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889p + p2 = -0.9722222222 + 0.03780864200 Combine like terms: -0.9722222222 + 0.03780864200 = -0.9344135802 0.03780864200 + 0.3888888889p + p2 = -0.9344135802 Factor a perfect square on the left side: (p + 0.1944444445)(p + 0.1944444445) = -0.9344135802 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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