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Simplifying 8p2 + -7p + -12 = 0 Reorder the terms: -12 + -7p + 8p2 = 0 Solving -12 + -7p + 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'. -1.5 + -0.875p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.875p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.875p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.875p + p2 = 0 + 1.5 -0.875p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.875p + p2 = 1.5 The p term is -0.875p. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875p + 0.19140625 + p2 = 1.5 + 0.19140625 Reorder the terms: 0.19140625 + -0.875p + p2 = 1.5 + 0.19140625 Combine like terms: 1.5 + 0.19140625 = 1.69140625 0.19140625 + -0.875p + p2 = 1.69140625 Factor a perfect square on the left side: (p + -0.4375)(p + -0.4375) = 1.69140625 Calculate the square root of the right side: 1.300540753 Break this problem into two subproblems by setting (p + -0.4375) equal to 1.300540753 and -1.300540753.Subproblem 1
p + -0.4375 = 1.300540753 Simplifying p + -0.4375 = 1.300540753 Reorder the terms: -0.4375 + p = 1.300540753 Solving -0.4375 + p = 1.300540753 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + p = 1.300540753 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + p = 1.300540753 + 0.4375 p = 1.300540753 + 0.4375 Combine like terms: 1.300540753 + 0.4375 = 1.738040753 p = 1.738040753 Simplifying p = 1.738040753Subproblem 2
p + -0.4375 = -1.300540753 Simplifying p + -0.4375 = -1.300540753 Reorder the terms: -0.4375 + p = -1.300540753 Solving -0.4375 + p = -1.300540753 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + p = -1.300540753 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + p = -1.300540753 + 0.4375 p = -1.300540753 + 0.4375 Combine like terms: -1.300540753 + 0.4375 = -0.863040753 p = -0.863040753 Simplifying p = -0.863040753Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.738040753, -0.863040753}
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