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Simplifying p2 + -13p = 0.40 Reorder the terms: -13p + p2 = 0.40 Solving -13p + p2 = 0.40 Solving for variable 'p'. Reorder the terms: -0.40 + -13p + p2 = 0.40 + -0.40 Combine like terms: 0.40 + -0.40 = 0.00 -0.40 + -13p + p2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.40' to each side of the equation. -0.40 + -13p + 0.40 + p2 = 0.00 + 0.40 Reorder the terms: -0.40 + 0.40 + -13p + p2 = 0.00 + 0.40 Combine like terms: -0.40 + 0.40 = 0.00 0.00 + -13p + p2 = 0.00 + 0.40 -13p + p2 = 0.00 + 0.40 Combine like terms: 0.00 + 0.40 = 0.4 -13p + p2 = 0.4 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 = 0.4 + 42.25 Reorder the terms: 42.25 + -13p + p2 = 0.4 + 42.25 Combine like terms: 0.4 + 42.25 = 42.65 42.25 + -13p + p2 = 42.65 Factor a perfect square on the left side: (p + -6.5)(p + -6.5) = 42.65 Calculate the square root of the right side: 6.530696747 Break this problem into two subproblems by setting (p + -6.5) equal to 6.530696747 and -6.530696747.Subproblem 1
p + -6.5 = 6.530696747 Simplifying p + -6.5 = 6.530696747 Reorder the terms: -6.5 + p = 6.530696747 Solving -6.5 + p = 6.530696747 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 = 6.530696747 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + p = 6.530696747 + 6.5 p = 6.530696747 + 6.5 Combine like terms: 6.530696747 + 6.5 = 13.030696747 p = 13.030696747 Simplifying p = 13.030696747Subproblem 2
p + -6.5 = -6.530696747 Simplifying p + -6.5 = -6.530696747 Reorder the terms: -6.5 + p = -6.530696747 Solving -6.5 + p = -6.530696747 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 = -6.530696747 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + p = -6.530696747 + 6.5 p = -6.530696747 + 6.5 Combine like terms: -6.530696747 + 6.5 = -0.030696747 p = -0.030696747 Simplifying p = -0.030696747Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.030696747, -0.030696747}
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