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Simplifying 5p + -9p3 + 8p2 + 45 + -9(p3 + 8p + 5) = 0 Reorder the terms: 5p + -9p3 + 8p2 + 45 + -9(5 + 8p + p3) = 0 5p + -9p3 + 8p2 + 45 + (5 * -9 + 8p * -9 + p3 * -9) = 0 5p + -9p3 + 8p2 + 45 + (-45 + -72p + -9p3) = 0 Reorder the terms: 45 + -45 + 5p + -72p + 8p2 + -9p3 + -9p3 = 0 Combine like terms: 45 + -45 = 0 0 + 5p + -72p + 8p2 + -9p3 + -9p3 = 0 5p + -72p + 8p2 + -9p3 + -9p3 = 0 Combine like terms: 5p + -72p = -67p -67p + 8p2 + -9p3 + -9p3 = 0 Combine like terms: -9p3 + -9p3 = -18p3 -67p + 8p2 + -18p3 = 0 Solving -67p + 8p2 + -18p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-67 + 8p + -18p2) = 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 '(-67 + 8p + -18p2)' equal to zero and attempt to solve: Simplifying -67 + 8p + -18p2 = 0 Solving -67 + 8p + -18p2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 3.722222222 + -0.4444444444p + p2 = 0 Move the constant term to the right: Add '-3.722222222' to each side of the equation. 3.722222222 + -0.4444444444p + -3.722222222 + p2 = 0 + -3.722222222 Reorder the terms: 3.722222222 + -3.722222222 + -0.4444444444p + p2 = 0 + -3.722222222 Combine like terms: 3.722222222 + -3.722222222 = 0.000000000 0.000000000 + -0.4444444444p + p2 = 0 + -3.722222222 -0.4444444444p + p2 = 0 + -3.722222222 Combine like terms: 0 + -3.722222222 = -3.722222222 -0.4444444444p + p2 = -3.722222222 The p term is -0.4444444444p. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444p + 0.04938271604 + p2 = -3.722222222 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444p + p2 = -3.722222222 + 0.04938271604 Combine like terms: -3.722222222 + 0.04938271604 = -3.67283950596 0.04938271604 + -0.4444444444p + p2 = -3.67283950596 Factor a perfect square on the left side: (p + -0.2222222222)(p + -0.2222222222) = -3.67283950596 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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