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Simplifying 3p2 + 18p + -1 = 0 Reorder the terms: -1 + 18p + 3p2 = 0 Solving -1 + 18p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 6p + p2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 6p + 0.3333333333 + p2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 6p + p2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 6p + p2 = 0 + 0.3333333333 6p + p2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 6p + p2 = 0.3333333333 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 0.3333333333 + 9 Reorder the terms: 9 + 6p + p2 = 0.3333333333 + 9 Combine like terms: 0.3333333333 + 9 = 9.3333333333 9 + 6p + p2 = 9.3333333333 Factor a perfect square on the left side: (p + 3)(p + 3) = 9.3333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (p + 3) equal to 3.055050463 and -3.055050463.Subproblem 1
p + 3 = 3.055050463 Simplifying p + 3 = 3.055050463 Reorder the terms: 3 + p = 3.055050463 Solving 3 + p = 3.055050463 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 3.055050463 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.055050463 + -3 p = 3.055050463 + -3 Combine like terms: 3.055050463 + -3 = 0.055050463 p = 0.055050463 Simplifying p = 0.055050463Subproblem 2
p + 3 = -3.055050463 Simplifying p + 3 = -3.055050463 Reorder the terms: 3 + p = -3.055050463 Solving 3 + p = -3.055050463 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -3.055050463 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.055050463 + -3 p = -3.055050463 + -3 Combine like terms: -3.055050463 + -3 = -6.055050463 p = -6.055050463 Simplifying p = -6.055050463Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.055050463, -6.055050463}
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