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Simplifying p2 + 15p + -50 = 0 Reorder the terms: -50 + 15p + p2 = 0 Solving -50 + 15p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 15p + 50 + p2 = 0 + 50 Reorder the terms: -50 + 50 + 15p + p2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 15p + p2 = 0 + 50 15p + p2 = 0 + 50 Combine like terms: 0 + 50 = 50 15p + p2 = 50 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 = 50 + 56.25 Reorder the terms: 56.25 + 15p + p2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + 15p + p2 = 106.25 Factor a perfect square on the left side: (p + 7.5)(p + 7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (p + 7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
p + 7.5 = 10.307764064 Simplifying p + 7.5 = 10.307764064 Reorder the terms: 7.5 + p = 10.307764064 Solving 7.5 + p = 10.307764064 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 = 10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + p = 10.307764064 + -7.5 p = 10.307764064 + -7.5 Combine like terms: 10.307764064 + -7.5 = 2.807764064 p = 2.807764064 Simplifying p = 2.807764064Subproblem 2
p + 7.5 = -10.307764064 Simplifying p + 7.5 = -10.307764064 Reorder the terms: 7.5 + p = -10.307764064 Solving 7.5 + p = -10.307764064 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 = -10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + p = -10.307764064 + -7.5 p = -10.307764064 + -7.5 Combine like terms: -10.307764064 + -7.5 = -17.807764064 p = -17.807764064 Simplifying p = -17.807764064Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.807764064, -17.807764064}
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