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Simplifying p2 + 16p + -6 = 16 Reorder the terms: -6 + 16p + p2 = 16 Solving -6 + 16p + p2 = 16 Solving for variable 'p'. Reorder the terms: -6 + -16 + 16p + p2 = 16 + -16 Combine like terms: -6 + -16 = -22 -22 + 16p + p2 = 16 + -16 Combine like terms: 16 + -16 = 0 -22 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 16p + 22 + p2 = 0 + 22 Reorder the terms: -22 + 22 + 16p + p2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 16p + p2 = 0 + 22 16p + p2 = 0 + 22 Combine like terms: 0 + 22 = 22 16p + p2 = 22 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 = 22 + 64 Reorder the terms: 64 + 16p + p2 = 22 + 64 Combine like terms: 22 + 64 = 86 64 + 16p + p2 = 86 Factor a perfect square on the left side: (p + 8)(p + 8) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (p + 8) equal to 9.273618495 and -9.273618495.Subproblem 1
p + 8 = 9.273618495 Simplifying p + 8 = 9.273618495 Reorder the terms: 8 + p = 9.273618495 Solving 8 + p = 9.273618495 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 = 9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + p = 9.273618495 + -8 p = 9.273618495 + -8 Combine like terms: 9.273618495 + -8 = 1.273618495 p = 1.273618495 Simplifying p = 1.273618495Subproblem 2
p + 8 = -9.273618495 Simplifying p + 8 = -9.273618495 Reorder the terms: 8 + p = -9.273618495 Solving 8 + p = -9.273618495 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 = -9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + p = -9.273618495 + -8 p = -9.273618495 + -8 Combine like terms: -9.273618495 + -8 = -17.273618495 p = -17.273618495 Simplifying p = -17.273618495Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.273618495, -17.273618495}
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