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Simplifying p2 + 18p = -11 Reorder the terms: 18p + p2 = -11 Solving 18p + p2 = -11 Solving for variable 'p'. Reorder the terms: 11 + 18p + p2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + 18p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 18p + -11 + p2 = 0 + -11 Reorder the terms: 11 + -11 + 18p + p2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 18p + p2 = 0 + -11 18p + p2 = 0 + -11 Combine like terms: 0 + -11 = -11 18p + p2 = -11 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 = -11 + 81 Reorder the terms: 81 + 18p + p2 = -11 + 81 Combine like terms: -11 + 81 = 70 81 + 18p + p2 = 70 Factor a perfect square on the left side: (p + 9)(p + 9) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (p + 9) equal to 8.366600265 and -8.366600265.Subproblem 1
p + 9 = 8.366600265 Simplifying p + 9 = 8.366600265 Reorder the terms: 9 + p = 8.366600265 Solving 9 + p = 8.366600265 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 = 8.366600265 + -9 Combine like terms: 9 + -9 = 0 0 + p = 8.366600265 + -9 p = 8.366600265 + -9 Combine like terms: 8.366600265 + -9 = -0.633399735 p = -0.633399735 Simplifying p = -0.633399735Subproblem 2
p + 9 = -8.366600265 Simplifying p + 9 = -8.366600265 Reorder the terms: 9 + p = -8.366600265 Solving 9 + p = -8.366600265 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 = -8.366600265 + -9 Combine like terms: 9 + -9 = 0 0 + p = -8.366600265 + -9 p = -8.366600265 + -9 Combine like terms: -8.366600265 + -9 = -17.366600265 p = -17.366600265 Simplifying p = -17.366600265Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.633399735, -17.366600265}
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