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Simplifying p2 + 16p = 41 Reorder the terms: 16p + p2 = 41 Solving 16p + p2 = 41 Solving for variable 'p'. Reorder the terms: -41 + 16p + p2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 16p + 41 + p2 = 0 + 41 Reorder the terms: -41 + 41 + 16p + p2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 16p + p2 = 0 + 41 16p + p2 = 0 + 41 Combine like terms: 0 + 41 = 41 16p + p2 = 41 The p term is 16p. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16p + 64 + p2 = 41 + 64 Reorder the terms: 64 + 16p + p2 = 41 + 64 Combine like terms: 41 + 64 = 105 64 + 16p + p2 = 105 Factor a perfect square on the left side: (p + 8)(p + 8) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (p + 8) equal to 10.246950766 and -10.246950766.Subproblem 1
p + 8 = 10.246950766 Simplifying p + 8 = 10.246950766 Reorder the terms: 8 + p = 10.246950766 Solving 8 + p = 10.246950766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = 10.246950766 + -8 Combine like terms: 8 + -8 = 0 0 + p = 10.246950766 + -8 p = 10.246950766 + -8 Combine like terms: 10.246950766 + -8 = 2.246950766 p = 2.246950766 Simplifying p = 2.246950766Subproblem 2
p + 8 = -10.246950766 Simplifying p + 8 = -10.246950766 Reorder the terms: 8 + p = -10.246950766 Solving 8 + p = -10.246950766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = -10.246950766 + -8 Combine like terms: 8 + -8 = 0 0 + p = -10.246950766 + -8 p = -10.246950766 + -8 Combine like terms: -10.246950766 + -8 = -18.246950766 p = -18.246950766 Simplifying p = -18.246950766Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.246950766, -18.246950766}
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