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Simplifying p2 + 16p = 4 Reorder the terms: 16p + p2 = 4 Solving 16p + p2 = 4 Solving for variable 'p'. Reorder the terms: -4 + 16p + p2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 16p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 16p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + 16p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 16p + p2 = 0 + 4 16p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 16p + p2 = 4 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 = 4 + 64 Reorder the terms: 64 + 16p + p2 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + 16p + p2 = 68 Factor a perfect square on the left side: (p + 8)(p + 8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (p + 8) equal to 8.246211251 and -8.246211251.Subproblem 1
p + 8 = 8.246211251 Simplifying p + 8 = 8.246211251 Reorder the terms: 8 + p = 8.246211251 Solving 8 + p = 8.246211251 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 = 8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + p = 8.246211251 + -8 p = 8.246211251 + -8 Combine like terms: 8.246211251 + -8 = 0.246211251 p = 0.246211251 Simplifying p = 0.246211251Subproblem 2
p + 8 = -8.246211251 Simplifying p + 8 = -8.246211251 Reorder the terms: 8 + p = -8.246211251 Solving 8 + p = -8.246211251 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 = -8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + p = -8.246211251 + -8 p = -8.246211251 + -8 Combine like terms: -8.246211251 + -8 = -16.246211251 p = -16.246211251 Simplifying p = -16.246211251Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.246211251, -16.246211251}
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