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Simplifying 8p2 + -16p + -5 = 0 Reorder the terms: -5 + -16p + 8p2 = 0 Solving -5 + -16p + 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'. -0.625 + -2p + p2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2p + 0.625 + p2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2p + p2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2p + p2 = 0 + 0.625 -2p + p2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2p + p2 = 0.625 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 0.625 + 1 Reorder the terms: 1 + -2p + p2 = 0.625 + 1 Combine like terms: 0.625 + 1 = 1.625 1 + -2p + p2 = 1.625 Factor a perfect square on the left side: (p + -1)(p + -1) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (p + -1) equal to 1.274754878 and -1.274754878.Subproblem 1
p + -1 = 1.274754878 Simplifying p + -1 = 1.274754878 Reorder the terms: -1 + p = 1.274754878 Solving -1 + p = 1.274754878 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + p = 1.274754878 + 1 p = 1.274754878 + 1 Combine like terms: 1.274754878 + 1 = 2.274754878 p = 2.274754878 Simplifying p = 2.274754878Subproblem 2
p + -1 = -1.274754878 Simplifying p + -1 = -1.274754878 Reorder the terms: -1 + p = -1.274754878 Solving -1 + p = -1.274754878 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + p = -1.274754878 + 1 p = -1.274754878 + 1 Combine like terms: -1.274754878 + 1 = -0.274754878 p = -0.274754878 Simplifying p = -0.274754878Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.274754878, -0.274754878}
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