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Simplifying 3p2 + 18p + 9 = 81 Reorder the terms: 9 + 18p + 3p2 = 81 Solving 9 + 18p + 3p2 = 81 Solving for variable 'p'. Reorder the terms: 9 + -81 + 18p + 3p2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + 18p + 3p2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + 18p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + 6p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + 6p + p2)' equal to zero and attempt to solve: Simplifying -24 + 6p + p2 = 0 Solving -24 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 6p + 24 + p2 = 0 + 24 Reorder the terms: -24 + 24 + 6p + p2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6p + p2 = 0 + 24 6p + p2 = 0 + 24 Combine like terms: 0 + 24 = 24 6p + p2 = 24 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 24 + 9 Reorder the terms: 9 + 6p + p2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + 6p + p2 = 33 Factor a perfect square on the left side: (p + 3)(p + 3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (p + 3) equal to 5.744562647 and -5.744562647.Subproblem 1
p + 3 = 5.744562647 Simplifying p + 3 = 5.744562647 Reorder the terms: 3 + p = 5.744562647 Solving 3 + p = 5.744562647 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + p = 5.744562647 + -3 p = 5.744562647 + -3 Combine like terms: 5.744562647 + -3 = 2.744562647 p = 2.744562647 Simplifying p = 2.744562647Subproblem 2
p + 3 = -5.744562647 Simplifying p + 3 = -5.744562647 Reorder the terms: 3 + p = -5.744562647 Solving 3 + p = -5.744562647 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + p = -5.744562647 + -3 p = -5.744562647 + -3 Combine like terms: -5.744562647 + -3 = -8.744562647 p = -8.744562647 Simplifying p = -8.744562647Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.744562647, -8.744562647}Solution
p = {2.744562647, -8.744562647}
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