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Simplifying p2 + 16p + -2 = 0 Reorder the terms: -2 + 16p + p2 = 0 Solving -2 + 16p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 16p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 16p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 16p + p2 = 0 + 2 16p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 16p + p2 = 2 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 = 2 + 64 Reorder the terms: 64 + 16p + p2 = 2 + 64 Combine like terms: 2 + 64 = 66 64 + 16p + p2 = 66 Factor a perfect square on the left side: (p + 8)(p + 8) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (p + 8) equal to 8.124038405 and -8.124038405.Subproblem 1
p + 8 = 8.124038405 Simplifying p + 8 = 8.124038405 Reorder the terms: 8 + p = 8.124038405 Solving 8 + p = 8.124038405 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 = 8.124038405 + -8 Combine like terms: 8 + -8 = 0 0 + p = 8.124038405 + -8 p = 8.124038405 + -8 Combine like terms: 8.124038405 + -8 = 0.124038405 p = 0.124038405 Simplifying p = 0.124038405Subproblem 2
p + 8 = -8.124038405 Simplifying p + 8 = -8.124038405 Reorder the terms: 8 + p = -8.124038405 Solving 8 + p = -8.124038405 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 = -8.124038405 + -8 Combine like terms: 8 + -8 = 0 0 + p = -8.124038405 + -8 p = -8.124038405 + -8 Combine like terms: -8.124038405 + -8 = -16.124038405 p = -16.124038405 Simplifying p = -16.124038405Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.124038405, -16.124038405}
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