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Simplifying 12p2 + -11p + -21 = 0 Reorder the terms: -21 + -11p + 12p2 = 0 Solving -21 + -11p + 12p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.75 + -0.9166666667p + p2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.9166666667p + 1.75 + p2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.9166666667p + p2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.9166666667p + p2 = 0 + 1.75 -0.9166666667p + p2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.9166666667p + p2 = 1.75 The p term is -0.9166666667p. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667p + 0.2100694445 + p2 = 1.75 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667p + p2 = 1.75 + 0.2100694445 Combine like terms: 1.75 + 0.2100694445 = 1.9600694445 0.2100694445 + -0.9166666667p + p2 = 1.9600694445 Factor a perfect square on the left side: (p + -0.4583333334)(p + -0.4583333334) = 1.9600694445 Calculate the square root of the right side: 1.400024801 Break this problem into two subproblems by setting (p + -0.4583333334) equal to 1.400024801 and -1.400024801.Subproblem 1
p + -0.4583333334 = 1.400024801 Simplifying p + -0.4583333334 = 1.400024801 Reorder the terms: -0.4583333334 + p = 1.400024801 Solving -0.4583333334 + p = 1.400024801 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + p = 1.400024801 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + p = 1.400024801 + 0.4583333334 p = 1.400024801 + 0.4583333334 Combine like terms: 1.400024801 + 0.4583333334 = 1.8583581344 p = 1.8583581344 Simplifying p = 1.8583581344Subproblem 2
p + -0.4583333334 = -1.400024801 Simplifying p + -0.4583333334 = -1.400024801 Reorder the terms: -0.4583333334 + p = -1.400024801 Solving -0.4583333334 + p = -1.400024801 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + p = -1.400024801 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + p = -1.400024801 + 0.4583333334 p = -1.400024801 + 0.4583333334 Combine like terms: -1.400024801 + 0.4583333334 = -0.9416914676 p = -0.9416914676 Simplifying p = -0.9416914676Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.8583581344, -0.9416914676}
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