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Simplifying 8p2 + 2p + -25 = 0 Reorder the terms: -25 + 2p + 8p2 = 0 Solving -25 + 2p + 8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 0.25p + p2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 0.25p + 3.125 + p2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 0.25p + p2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 0.25p + p2 = 0 + 3.125 0.25p + p2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 0.25p + p2 = 3.125 The p term is 0.25p. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25p + 0.015625 + p2 = 3.125 + 0.015625 Reorder the terms: 0.015625 + 0.25p + p2 = 3.125 + 0.015625 Combine like terms: 3.125 + 0.015625 = 3.140625 0.015625 + 0.25p + p2 = 3.140625 Factor a perfect square on the left side: (p + 0.125)(p + 0.125) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (p + 0.125) equal to 1.77218086 and -1.77218086.Subproblem 1
p + 0.125 = 1.77218086 Simplifying p + 0.125 = 1.77218086 Reorder the terms: 0.125 + p = 1.77218086 Solving 0.125 + p = 1.77218086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = 1.77218086 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = 1.77218086 + -0.125 p = 1.77218086 + -0.125 Combine like terms: 1.77218086 + -0.125 = 1.64718086 p = 1.64718086 Simplifying p = 1.64718086Subproblem 2
p + 0.125 = -1.77218086 Simplifying p + 0.125 = -1.77218086 Reorder the terms: 0.125 + p = -1.77218086 Solving 0.125 + p = -1.77218086 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = -1.77218086 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = -1.77218086 + -0.125 p = -1.77218086 + -0.125 Combine like terms: -1.77218086 + -0.125 = -1.89718086 p = -1.89718086 Simplifying p = -1.89718086Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.64718086, -1.89718086}
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