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Simplifying p2 + -15p + 20 = 0 Reorder the terms: 20 + -15p + p2 = 0 Solving 20 + -15p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -15p + -20 + p2 = 0 + -20 Reorder the terms: 20 + -20 + -15p + p2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -15p + p2 = 0 + -20 -15p + p2 = 0 + -20 Combine like terms: 0 + -20 = -20 -15p + p2 = -20 The p term is -15p. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15p + 56.25 + p2 = -20 + 56.25 Reorder the terms: 56.25 + -15p + p2 = -20 + 56.25 Combine like terms: -20 + 56.25 = 36.25 56.25 + -15p + p2 = 36.25 Factor a perfect square on the left side: (p + -7.5)(p + -7.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (p + -7.5) equal to 6.020797289 and -6.020797289.Subproblem 1
p + -7.5 = 6.020797289 Simplifying p + -7.5 = 6.020797289 Reorder the terms: -7.5 + p = 6.020797289 Solving -7.5 + p = 6.020797289 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = 6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = 6.020797289 + 7.5 p = 6.020797289 + 7.5 Combine like terms: 6.020797289 + 7.5 = 13.520797289 p = 13.520797289 Simplifying p = 13.520797289Subproblem 2
p + -7.5 = -6.020797289 Simplifying p + -7.5 = -6.020797289 Reorder the terms: -7.5 + p = -6.020797289 Solving -7.5 + p = -6.020797289 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = -6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = -6.020797289 + 7.5 p = -6.020797289 + 7.5 Combine like terms: -6.020797289 + 7.5 = 1.479202711 p = 1.479202711 Simplifying p = 1.479202711Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.520797289, 1.479202711}
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