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Simplifying p2 + 4p + -54 = -10 Reorder the terms: -54 + 4p + p2 = -10 Solving -54 + 4p + p2 = -10 Solving for variable 'p'. Reorder the terms: -54 + 10 + 4p + p2 = -10 + 10 Combine like terms: -54 + 10 = -44 -44 + 4p + p2 = -10 + 10 Combine like terms: -10 + 10 = 0 -44 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 4p + 44 + p2 = 0 + 44 Reorder the terms: -44 + 44 + 4p + p2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 4p + p2 = 0 + 44 4p + p2 = 0 + 44 Combine like terms: 0 + 44 = 44 4p + p2 = 44 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 44 + 4 Reorder the terms: 4 + 4p + p2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + 4p + p2 = 48 Factor a perfect square on the left side: (p + 2)(p + 2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (p + 2) equal to 6.92820323 and -6.92820323.Subproblem 1
p + 2 = 6.92820323 Simplifying p + 2 = 6.92820323 Reorder the terms: 2 + p = 6.92820323 Solving 2 + p = 6.92820323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + p = 6.92820323 + -2 p = 6.92820323 + -2 Combine like terms: 6.92820323 + -2 = 4.92820323 p = 4.92820323 Simplifying p = 4.92820323Subproblem 2
p + 2 = -6.92820323 Simplifying p + 2 = -6.92820323 Reorder the terms: 2 + p = -6.92820323 Solving 2 + p = -6.92820323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + p = -6.92820323 + -2 p = -6.92820323 + -2 Combine like terms: -6.92820323 + -2 = -8.92820323 p = -8.92820323 Simplifying p = -8.92820323Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.92820323, -8.92820323}
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