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Simplifying p2 + 12p + 30 = 0 Reorder the terms: 30 + 12p + p2 = 0 Solving 30 + 12p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 12p + -30 + p2 = 0 + -30 Reorder the terms: 30 + -30 + 12p + p2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 12p + p2 = 0 + -30 12p + p2 = 0 + -30 Combine like terms: 0 + -30 = -30 12p + p2 = -30 The p term is 12p. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12p + 36 + p2 = -30 + 36 Reorder the terms: 36 + 12p + p2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + 12p + p2 = 6 Factor a perfect square on the left side: (p + 6)(p + 6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (p + 6) equal to 2.449489743 and -2.449489743.Subproblem 1
p + 6 = 2.449489743 Simplifying p + 6 = 2.449489743 Reorder the terms: 6 + p = 2.449489743 Solving 6 + p = 2.449489743 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = 2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + p = 2.449489743 + -6 p = 2.449489743 + -6 Combine like terms: 2.449489743 + -6 = -3.550510257 p = -3.550510257 Simplifying p = -3.550510257Subproblem 2
p + 6 = -2.449489743 Simplifying p + 6 = -2.449489743 Reorder the terms: 6 + p = -2.449489743 Solving 6 + p = -2.449489743 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + p = -2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + p = -2.449489743 + -6 p = -2.449489743 + -6 Combine like terms: -2.449489743 + -6 = -8.449489743 p = -8.449489743 Simplifying p = -8.449489743Solution
The solution to the problem is based on the solutions from the subproblems. p = {-3.550510257, -8.449489743}
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