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Simplifying p2 = -13p + 40 Reorder the terms: p2 = 40 + -13p Solving p2 = 40 + -13p Solving for variable 'p'. Reorder the terms: -40 + 13p + p2 = 40 + -13p + -40 + 13p Reorder the terms: -40 + 13p + p2 = 40 + -40 + -13p + 13p Combine like terms: 40 + -40 = 0 -40 + 13p + p2 = 0 + -13p + 13p -40 + 13p + p2 = -13p + 13p Combine like terms: -13p + 13p = 0 -40 + 13p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 13p + 40 + p2 = 0 + 40 Reorder the terms: -40 + 40 + 13p + p2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 13p + p2 = 0 + 40 13p + p2 = 0 + 40 Combine like terms: 0 + 40 = 40 13p + p2 = 40 The p term is 13p. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13p + 42.25 + p2 = 40 + 42.25 Reorder the terms: 42.25 + 13p + p2 = 40 + 42.25 Combine like terms: 40 + 42.25 = 82.25 42.25 + 13p + p2 = 82.25 Factor a perfect square on the left side: (p + 6.5)(p + 6.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (p + 6.5) equal to 9.069178574 and -9.069178574.Subproblem 1
p + 6.5 = 9.069178574 Simplifying p + 6.5 = 9.069178574 Reorder the terms: 6.5 + p = 9.069178574 Solving 6.5 + p = 9.069178574 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + p = 9.069178574 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + p = 9.069178574 + -6.5 p = 9.069178574 + -6.5 Combine like terms: 9.069178574 + -6.5 = 2.569178574 p = 2.569178574 Simplifying p = 2.569178574Subproblem 2
p + 6.5 = -9.069178574 Simplifying p + 6.5 = -9.069178574 Reorder the terms: 6.5 + p = -9.069178574 Solving 6.5 + p = -9.069178574 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + p = -9.069178574 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + p = -9.069178574 + -6.5 p = -9.069178574 + -6.5 Combine like terms: -9.069178574 + -6.5 = -15.569178574 p = -15.569178574 Simplifying p = -15.569178574Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.569178574, -15.569178574}
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