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Simplifying p2 + 12p + -40 = 0 Reorder the terms: -40 + 12p + p2 = 0 Solving -40 + 12p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 12p + 40 + p2 = 0 + 40 Reorder the terms: -40 + 40 + 12p + p2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 12p + p2 = 0 + 40 12p + p2 = 0 + 40 Combine like terms: 0 + 40 = 40 12p + p2 = 40 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 = 40 + 36 Reorder the terms: 36 + 12p + p2 = 40 + 36 Combine like terms: 40 + 36 = 76 36 + 12p + p2 = 76 Factor a perfect square on the left side: (p + 6)(p + 6) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (p + 6) equal to 8.717797887 and -8.717797887.Subproblem 1
p + 6 = 8.717797887 Simplifying p + 6 = 8.717797887 Reorder the terms: 6 + p = 8.717797887 Solving 6 + p = 8.717797887 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 = 8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + p = 8.717797887 + -6 p = 8.717797887 + -6 Combine like terms: 8.717797887 + -6 = 2.717797887 p = 2.717797887 Simplifying p = 2.717797887Subproblem 2
p + 6 = -8.717797887 Simplifying p + 6 = -8.717797887 Reorder the terms: 6 + p = -8.717797887 Solving 6 + p = -8.717797887 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 = -8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + p = -8.717797887 + -6 p = -8.717797887 + -6 Combine like terms: -8.717797887 + -6 = -14.717797887 p = -14.717797887 Simplifying p = -14.717797887Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.717797887, -14.717797887}
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