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Simplifying p3 + 8p2 = 18p Reorder the terms: 8p2 + p3 = 18p Solving 8p2 + p3 = 18p Solving for variable 'p'. Reorder the terms: -18p + 8p2 + p3 = 18p + -18p Combine like terms: 18p + -18p = 0 -18p + 8p2 + p3 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-18 + 8p + p2) = 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 '(-18 + 8p + p2)' equal to zero and attempt to solve: Simplifying -18 + 8p + p2 = 0 Solving -18 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 8p + 18 + p2 = 0 + 18 Reorder the terms: -18 + 18 + 8p + p2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8p + p2 = 0 + 18 8p + p2 = 0 + 18 Combine like terms: 0 + 18 = 18 8p + p2 = 18 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 18 + 16 Reorder the terms: 16 + 8p + p2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + 8p + p2 = 34 Factor a perfect square on the left side: (p + 4)(p + 4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (p + 4) equal to 5.830951895 and -5.830951895.Subproblem 1
p + 4 = 5.830951895 Simplifying p + 4 = 5.830951895 Reorder the terms: 4 + p = 5.830951895 Solving 4 + p = 5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + p = 5.830951895 + -4 p = 5.830951895 + -4 Combine like terms: 5.830951895 + -4 = 1.830951895 p = 1.830951895 Simplifying p = 1.830951895Subproblem 2
p + 4 = -5.830951895 Simplifying p + 4 = -5.830951895 Reorder the terms: 4 + p = -5.830951895 Solving 4 + p = -5.830951895 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + p = -5.830951895 + -4 p = -5.830951895 + -4 Combine like terms: -5.830951895 + -4 = -9.830951895 p = -9.830951895 Simplifying p = -9.830951895Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.830951895, -9.830951895}Solution
p = {0, 1.830951895, -9.830951895}
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