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Simplifying 15p + 3p2 = 20 Solving 15p + 3p2 = 20 Solving for variable 'p'. Reorder the terms: -20 + 15p + 3p2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 15p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + 5p + p2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 5p + 6.666666667 + p2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 5p + p2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 5p + p2 = 0 + 6.666666667 5p + p2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 5p + p2 = 6.666666667 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 6.666666667 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 6.666666667 + 6.25 Combine like terms: 6.666666667 + 6.25 = 12.916666667 6.25 + 5p + p2 = 12.916666667 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 12.916666667 Calculate the square root of the right side: 3.593976442 Break this problem into two subproblems by setting (p + 2.5) equal to 3.593976442 and -3.593976442.Subproblem 1
p + 2.5 = 3.593976442 Simplifying p + 2.5 = 3.593976442 Reorder the terms: 2.5 + p = 3.593976442 Solving 2.5 + p = 3.593976442 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 3.593976442 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 3.593976442 + -2.5 p = 3.593976442 + -2.5 Combine like terms: 3.593976442 + -2.5 = 1.093976442 p = 1.093976442 Simplifying p = 1.093976442Subproblem 2
p + 2.5 = -3.593976442 Simplifying p + 2.5 = -3.593976442 Reorder the terms: 2.5 + p = -3.593976442 Solving 2.5 + p = -3.593976442 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -3.593976442 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -3.593976442 + -2.5 p = -3.593976442 + -2.5 Combine like terms: -3.593976442 + -2.5 = -6.093976442 p = -6.093976442 Simplifying p = -6.093976442Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.093976442, -6.093976442}
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