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Simplifying 3p2 + 243p = 81 Reorder the terms: 243p + 3p2 = 81 Solving 243p + 3p2 = 81 Solving for variable 'p'. Reorder the terms: -81 + 243p + 3p2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 243p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 81p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + 81p + p2)' equal to zero and attempt to solve: Simplifying -27 + 81p + p2 = 0 Solving -27 + 81p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 81p + 27 + p2 = 0 + 27 Reorder the terms: -27 + 27 + 81p + p2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 81p + p2 = 0 + 27 81p + p2 = 0 + 27 Combine like terms: 0 + 27 = 27 81p + p2 = 27 The p term is 81p. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81p + 1640.25 + p2 = 27 + 1640.25 Reorder the terms: 1640.25 + 81p + p2 = 27 + 1640.25 Combine like terms: 27 + 1640.25 = 1667.25 1640.25 + 81p + p2 = 1667.25 Factor a perfect square on the left side: (p + 40.5)(p + 40.5) = 1667.25 Calculate the square root of the right side: 40.831972766 Break this problem into two subproblems by setting (p + 40.5) equal to 40.831972766 and -40.831972766.Subproblem 1
p + 40.5 = 40.831972766 Simplifying p + 40.5 = 40.831972766 Reorder the terms: 40.5 + p = 40.831972766 Solving 40.5 + p = 40.831972766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + p = 40.831972766 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + p = 40.831972766 + -40.5 p = 40.831972766 + -40.5 Combine like terms: 40.831972766 + -40.5 = 0.331972766 p = 0.331972766 Simplifying p = 0.331972766Subproblem 2
p + 40.5 = -40.831972766 Simplifying p + 40.5 = -40.831972766 Reorder the terms: 40.5 + p = -40.831972766 Solving 40.5 + p = -40.831972766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + p = -40.831972766 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + p = -40.831972766 + -40.5 p = -40.831972766 + -40.5 Combine like terms: -40.831972766 + -40.5 = -81.331972766 p = -81.331972766 Simplifying p = -81.331972766Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.331972766, -81.331972766}Solution
p = {0.331972766, -81.331972766}
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