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Simplifying p2 + 16p = 33 Reorder the terms: 16p + p2 = 33 Solving 16p + p2 = 33 Solving for variable 'p'. Reorder the terms: -33 + 16p + p2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 16p + 33 + p2 = 0 + 33 Reorder the terms: -33 + 33 + 16p + p2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 16p + p2 = 0 + 33 16p + p2 = 0 + 33 Combine like terms: 0 + 33 = 33 16p + p2 = 33 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 = 33 + 64 Reorder the terms: 64 + 16p + p2 = 33 + 64 Combine like terms: 33 + 64 = 97 64 + 16p + p2 = 97 Factor a perfect square on the left side: (p + 8)(p + 8) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (p + 8) equal to 9.848857802 and -9.848857802.Subproblem 1
p + 8 = 9.848857802 Simplifying p + 8 = 9.848857802 Reorder the terms: 8 + p = 9.848857802 Solving 8 + p = 9.848857802 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 = 9.848857802 + -8 Combine like terms: 8 + -8 = 0 0 + p = 9.848857802 + -8 p = 9.848857802 + -8 Combine like terms: 9.848857802 + -8 = 1.848857802 p = 1.848857802 Simplifying p = 1.848857802Subproblem 2
p + 8 = -9.848857802 Simplifying p + 8 = -9.848857802 Reorder the terms: 8 + p = -9.848857802 Solving 8 + p = -9.848857802 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 = -9.848857802 + -8 Combine like terms: 8 + -8 = 0 0 + p = -9.848857802 + -8 p = -9.848857802 + -8 Combine like terms: -9.848857802 + -8 = -17.848857802 p = -17.848857802 Simplifying p = -17.848857802Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.848857802, -17.848857802}
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