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Simplifying 2p2 + p + -39 = 0 Reorder the terms: -39 + p + 2p2 = 0 Solving -39 + p + 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'. -19.5 + 0.5p + p2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + 0.5p + 19.5 + p2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + 0.5p + p2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + 0.5p + p2 = 0 + 19.5 0.5p + p2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 0.5p + p2 = 19.5 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5p + 0.25 + p2 = 19.5 + 0.25 Reorder the terms: 0.25 + 0.5p + p2 = 19.5 + 0.25 Combine like terms: 19.5 + 0.25 = 19.75 0.25 + 0.5p + p2 = 19.75 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (p + 0.5) equal to 4.444097209 and -4.444097209.Subproblem 1
p + 0.5 = 4.444097209 Simplifying p + 0.5 = 4.444097209 Reorder the terms: 0.5 + p = 4.444097209 Solving 0.5 + p = 4.444097209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 4.444097209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 4.444097209 + -0.5 p = 4.444097209 + -0.5 Combine like terms: 4.444097209 + -0.5 = 3.944097209 p = 3.944097209 Simplifying p = 3.944097209Subproblem 2
p + 0.5 = -4.444097209 Simplifying p + 0.5 = -4.444097209 Reorder the terms: 0.5 + p = -4.444097209 Solving 0.5 + p = -4.444097209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -4.444097209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -4.444097209 + -0.5 p = -4.444097209 + -0.5 Combine like terms: -4.444097209 + -0.5 = -4.944097209 p = -4.944097209 Simplifying p = -4.944097209Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.944097209, -4.944097209}
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