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Simplifying p2 + 18p + 6 = 0 Reorder the terms: 6 + 18p + p2 = 0 Solving 6 + 18p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 18p + -6 + p2 = 0 + -6 Reorder the terms: 6 + -6 + 18p + p2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 18p + p2 = 0 + -6 18p + p2 = 0 + -6 Combine like terms: 0 + -6 = -6 18p + p2 = -6 The p term is 18p. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18p + 81 + p2 = -6 + 81 Reorder the terms: 81 + 18p + p2 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + 18p + p2 = 75 Factor a perfect square on the left side: (p + 9)(p + 9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (p + 9) equal to 8.660254038 and -8.660254038.Subproblem 1
p + 9 = 8.660254038 Simplifying p + 9 = 8.660254038 Reorder the terms: 9 + p = 8.660254038 Solving 9 + p = 8.660254038 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = 8.660254038 + -9 Combine like terms: 9 + -9 = 0 0 + p = 8.660254038 + -9 p = 8.660254038 + -9 Combine like terms: 8.660254038 + -9 = -0.339745962 p = -0.339745962 Simplifying p = -0.339745962Subproblem 2
p + 9 = -8.660254038 Simplifying p + 9 = -8.660254038 Reorder the terms: 9 + p = -8.660254038 Solving 9 + p = -8.660254038 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = -8.660254038 + -9 Combine like terms: 9 + -9 = 0 0 + p = -8.660254038 + -9 p = -8.660254038 + -9 Combine like terms: -8.660254038 + -9 = -17.660254038 p = -17.660254038 Simplifying p = -17.660254038Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.339745962, -17.660254038}
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