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Simplifying 8p2 + -24p + 13 = 0 Reorder the terms: 13 + -24p + 8p2 = 0 Solving 13 + -24p + 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'. 1.625 + -3p + p2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -3p + -1.625 + p2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -3p + p2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -3p + p2 = 0 + -1.625 -3p + p2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -3p + p2 = -1.625 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = -1.625 + 2.25 Reorder the terms: 2.25 + -3p + p2 = -1.625 + 2.25 Combine like terms: -1.625 + 2.25 = 0.625 2.25 + -3p + p2 = 0.625 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (p + -1.5) equal to 0.790569415 and -0.790569415.Subproblem 1
p + -1.5 = 0.790569415 Simplifying p + -1.5 = 0.790569415 Reorder the terms: -1.5 + p = 0.790569415 Solving -1.5 + p = 0.790569415 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 0.790569415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 0.790569415 + 1.5 p = 0.790569415 + 1.5 Combine like terms: 0.790569415 + 1.5 = 2.290569415 p = 2.290569415 Simplifying p = 2.290569415Subproblem 2
p + -1.5 = -0.790569415 Simplifying p + -1.5 = -0.790569415 Reorder the terms: -1.5 + p = -0.790569415 Solving -1.5 + p = -0.790569415 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -0.790569415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -0.790569415 + 1.5 p = -0.790569415 + 1.5 Combine like terms: -0.790569415 + 1.5 = 0.709430585 p = 0.709430585 Simplifying p = 0.709430585Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.290569415, 0.709430585}
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