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Simplifying 18p3 + -63p2 + -9p = 0 Reorder the terms: -9p + -63p2 + 18p3 = 0 Solving -9p + -63p2 + 18p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '9p'. 9p(-1 + -7p + 2p2) = 0 Ignore the factor 9.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 '(-1 + -7p + 2p2)' equal to zero and attempt to solve: Simplifying -1 + -7p + 2p2 = 0 Solving -1 + -7p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -3.5p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.5p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.5p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.5p + p2 = 0 + 0.5 -3.5p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.5p + p2 = 0.5 The p term is -3.5p. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5p + 3.0625 + p2 = 0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5p + p2 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + -3.5p + p2 = 3.5625 Factor a perfect square on the left side: (p + -1.75)(p + -1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (p + -1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
p + -1.75 = 1.887458609 Simplifying p + -1.75 = 1.887458609 Reorder the terms: -1.75 + p = 1.887458609 Solving -1.75 + p = 1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = 1.887458609 + 1.75 p = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 p = 3.637458609 Simplifying p = 3.637458609Subproblem 2
p + -1.75 = -1.887458609 Simplifying p + -1.75 = -1.887458609 Reorder the terms: -1.75 + p = -1.887458609 Solving -1.75 + p = -1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + p = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + p = -1.887458609 + 1.75 p = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 p = -0.137458609 Simplifying p = -0.137458609Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.637458609, -0.137458609}Solution
p = {0, 3.637458609, -0.137458609}
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