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Simplifying 2p2 + 12p + 11 = 0 Reorder the terms: 11 + 12p + 2p2 = 0 Solving 11 + 12p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 6p + p2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 6p + -5.5 + p2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 6p + p2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 6p + p2 = 0 + -5.5 6p + p2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 6p + p2 = -5.5 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 = -5.5 + 9 Reorder the terms: 9 + 6p + p2 = -5.5 + 9 Combine like terms: -5.5 + 9 = 3.5 9 + 6p + p2 = 3.5 Factor a perfect square on the left side: (p + 3)(p + 3) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (p + 3) equal to 1.870828693 and -1.870828693.Subproblem 1
p + 3 = 1.870828693 Simplifying p + 3 = 1.870828693 Reorder the terms: 3 + p = 1.870828693 Solving 3 + p = 1.870828693 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 = 1.870828693 + -3 Combine like terms: 3 + -3 = 0 0 + p = 1.870828693 + -3 p = 1.870828693 + -3 Combine like terms: 1.870828693 + -3 = -1.129171307 p = -1.129171307 Simplifying p = -1.129171307Subproblem 2
p + 3 = -1.870828693 Simplifying p + 3 = -1.870828693 Reorder the terms: 3 + p = -1.870828693 Solving 3 + p = -1.870828693 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 = -1.870828693 + -3 Combine like terms: 3 + -3 = 0 0 + p = -1.870828693 + -3 p = -1.870828693 + -3 Combine like terms: -1.870828693 + -3 = -4.870828693 p = -4.870828693 Simplifying p = -4.870828693Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.129171307, -4.870828693}
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