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Simplifying p2 + 18p + 24 = -3 Reorder the terms: 24 + 18p + p2 = -3 Solving 24 + 18p + p2 = -3 Solving for variable 'p'. Reorder the terms: 24 + 3 + 18p + p2 = -3 + 3 Combine like terms: 24 + 3 = 27 27 + 18p + p2 = -3 + 3 Combine like terms: -3 + 3 = 0 27 + 18p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 18p + -27 + p2 = 0 + -27 Reorder the terms: 27 + -27 + 18p + p2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 18p + p2 = 0 + -27 18p + p2 = 0 + -27 Combine like terms: 0 + -27 = -27 18p + p2 = -27 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 = -27 + 81 Reorder the terms: 81 + 18p + p2 = -27 + 81 Combine like terms: -27 + 81 = 54 81 + 18p + p2 = 54 Factor a perfect square on the left side: (p + 9)(p + 9) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (p + 9) equal to 7.348469228 and -7.348469228.Subproblem 1
p + 9 = 7.348469228 Simplifying p + 9 = 7.348469228 Reorder the terms: 9 + p = 7.348469228 Solving 9 + p = 7.348469228 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 = 7.348469228 + -9 Combine like terms: 9 + -9 = 0 0 + p = 7.348469228 + -9 p = 7.348469228 + -9 Combine like terms: 7.348469228 + -9 = -1.651530772 p = -1.651530772 Simplifying p = -1.651530772Subproblem 2
p + 9 = -7.348469228 Simplifying p + 9 = -7.348469228 Reorder the terms: 9 + p = -7.348469228 Solving 9 + p = -7.348469228 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 = -7.348469228 + -9 Combine like terms: 9 + -9 = 0 0 + p = -7.348469228 + -9 p = -7.348469228 + -9 Combine like terms: -7.348469228 + -9 = -16.348469228 p = -16.348469228 Simplifying p = -16.348469228Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.651530772, -16.348469228}
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