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Simplifying p2 + 5p + -48 = 0 Reorder the terms: -48 + 5p + p2 = 0 Solving -48 + 5p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 5p + 48 + p2 = 0 + 48 Reorder the terms: -48 + 48 + 5p + p2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 5p + p2 = 0 + 48 5p + p2 = 0 + 48 Combine like terms: 0 + 48 = 48 5p + p2 = 48 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 = 48 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 48 + 6.25 Combine like terms: 48 + 6.25 = 54.25 6.25 + 5p + p2 = 54.25 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (p + 2.5) equal to 7.365459931 and -7.365459931.Subproblem 1
p + 2.5 = 7.365459931 Simplifying p + 2.5 = 7.365459931 Reorder the terms: 2.5 + p = 7.365459931 Solving 2.5 + p = 7.365459931 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 = 7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 7.365459931 + -2.5 p = 7.365459931 + -2.5 Combine like terms: 7.365459931 + -2.5 = 4.865459931 p = 4.865459931 Simplifying p = 4.865459931Subproblem 2
p + 2.5 = -7.365459931 Simplifying p + 2.5 = -7.365459931 Reorder the terms: 2.5 + p = -7.365459931 Solving 2.5 + p = -7.365459931 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 = -7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -7.365459931 + -2.5 p = -7.365459931 + -2.5 Combine like terms: -7.365459931 + -2.5 = -9.865459931 p = -9.865459931 Simplifying p = -9.865459931Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.865459931, -9.865459931}
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