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Simplifying 2p2 + 9p + 1 = 0 Reorder the terms: 1 + 9p + 2p2 = 0 Solving 1 + 9p + 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'. 0.5 + 4.5p + p2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4.5p + -0.5 + p2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4.5p + p2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4.5p + p2 = 0 + -0.5 4.5p + p2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4.5p + p2 = -0.5 The p term is 4.5p. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5p + 5.0625 + p2 = -0.5 + 5.0625 Reorder the terms: 5.0625 + 4.5p + p2 = -0.5 + 5.0625 Combine like terms: -0.5 + 5.0625 = 4.5625 5.0625 + 4.5p + p2 = 4.5625 Factor a perfect square on the left side: (p + 2.25)(p + 2.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (p + 2.25) equal to 2.136000936 and -2.136000936.Subproblem 1
p + 2.25 = 2.136000936 Simplifying p + 2.25 = 2.136000936 Reorder the terms: 2.25 + p = 2.136000936 Solving 2.25 + p = 2.136000936 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + p = 2.136000936 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + p = 2.136000936 + -2.25 p = 2.136000936 + -2.25 Combine like terms: 2.136000936 + -2.25 = -0.113999064 p = -0.113999064 Simplifying p = -0.113999064Subproblem 2
p + 2.25 = -2.136000936 Simplifying p + 2.25 = -2.136000936 Reorder the terms: 2.25 + p = -2.136000936 Solving 2.25 + p = -2.136000936 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + p = -2.136000936 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + p = -2.136000936 + -2.25 p = -2.136000936 + -2.25 Combine like terms: -2.136000936 + -2.25 = -4.386000936 p = -4.386000936 Simplifying p = -4.386000936Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.113999064, -4.386000936}
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