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Simplifying 2p2 + 14p + 11 = 0 Reorder the terms: 11 + 14p + 2p2 = 0 Solving 11 + 14p + 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 + 7p + p2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 7p + -5.5 + p2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 7p + p2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 7p + p2 = 0 + -5.5 7p + p2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 7p + p2 = -5.5 The p term is 7p. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7p + 12.25 + p2 = -5.5 + 12.25 Reorder the terms: 12.25 + 7p + p2 = -5.5 + 12.25 Combine like terms: -5.5 + 12.25 = 6.75 12.25 + 7p + p2 = 6.75 Factor a perfect square on the left side: (p + 3.5)(p + 3.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (p + 3.5) equal to 2.598076211 and -2.598076211.Subproblem 1
p + 3.5 = 2.598076211 Simplifying p + 3.5 = 2.598076211 Reorder the terms: 3.5 + p = 2.598076211 Solving 3.5 + p = 2.598076211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = 2.598076211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = 2.598076211 + -3.5 p = 2.598076211 + -3.5 Combine like terms: 2.598076211 + -3.5 = -0.901923789 p = -0.901923789 Simplifying p = -0.901923789Subproblem 2
p + 3.5 = -2.598076211 Simplifying p + 3.5 = -2.598076211 Reorder the terms: 3.5 + p = -2.598076211 Solving 3.5 + p = -2.598076211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = -2.598076211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = -2.598076211 + -3.5 p = -2.598076211 + -3.5 Combine like terms: -2.598076211 + -3.5 = -6.098076211 p = -6.098076211 Simplifying p = -6.098076211Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.901923789, -6.098076211}
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