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Simplifying p2 + 8p + 9 = 0 Reorder the terms: 9 + 8p + p2 = 0 Solving 9 + 8p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8p + -9 + p2 = 0 + -9 Reorder the terms: 9 + -9 + 8p + p2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8p + p2 = 0 + -9 8p + p2 = 0 + -9 Combine like terms: 0 + -9 = -9 8p + p2 = -9 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = -9 + 16 Reorder the terms: 16 + 8p + p2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8p + p2 = 7 Factor a perfect square on the left side: (p + 4)(p + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (p + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
p + 4 = 2.645751311 Simplifying p + 4 = 2.645751311 Reorder the terms: 4 + p = 2.645751311 Solving 4 + p = 2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + p = 2.645751311 + -4 p = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 p = -1.354248689 Simplifying p = -1.354248689Subproblem 2
p + 4 = -2.645751311 Simplifying p + 4 = -2.645751311 Reorder the terms: 4 + p = -2.645751311 Solving 4 + p = -2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + p = -2.645751311 + -4 p = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 p = -6.645751311 Simplifying p = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.354248689, -6.645751311}
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