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Simplifying p2 + 18p + -14 = 0 Reorder the terms: -14 + 18p + p2 = 0 Solving -14 + 18p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 18p + 14 + p2 = 0 + 14 Reorder the terms: -14 + 14 + 18p + p2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 18p + p2 = 0 + 14 18p + p2 = 0 + 14 Combine like terms: 0 + 14 = 14 18p + p2 = 14 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 = 14 + 81 Reorder the terms: 81 + 18p + p2 = 14 + 81 Combine like terms: 14 + 81 = 95 81 + 18p + p2 = 95 Factor a perfect square on the left side: (p + 9)(p + 9) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (p + 9) equal to 9.746794345 and -9.746794345.Subproblem 1
p + 9 = 9.746794345 Simplifying p + 9 = 9.746794345 Reorder the terms: 9 + p = 9.746794345 Solving 9 + p = 9.746794345 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 = 9.746794345 + -9 Combine like terms: 9 + -9 = 0 0 + p = 9.746794345 + -9 p = 9.746794345 + -9 Combine like terms: 9.746794345 + -9 = 0.746794345 p = 0.746794345 Simplifying p = 0.746794345Subproblem 2
p + 9 = -9.746794345 Simplifying p + 9 = -9.746794345 Reorder the terms: 9 + p = -9.746794345 Solving 9 + p = -9.746794345 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 = -9.746794345 + -9 Combine like terms: 9 + -9 = 0 0 + p = -9.746794345 + -9 p = -9.746794345 + -9 Combine like terms: -9.746794345 + -9 = -18.746794345 p = -18.746794345 Simplifying p = -18.746794345Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.746794345, -18.746794345}
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