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Simplifying 24p2 + -55p + -1 = 0 Reorder the terms: -1 + -55p + 24p2 = 0 Solving -1 + -55p + 24p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.04166666667 + -2.291666667p + p2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -2.291666667p + 0.04166666667 + p2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -2.291666667p + p2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -2.291666667p + p2 = 0 + 0.04166666667 -2.291666667p + p2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -2.291666667p + p2 = 0.04166666667 The p term is -2.291666667p. Take half its coefficient (-1.145833334). Square it (1.312934029) and add it to both sides. Add '1.312934029' to each side of the equation. -2.291666667p + 1.312934029 + p2 = 0.04166666667 + 1.312934029 Reorder the terms: 1.312934029 + -2.291666667p + p2 = 0.04166666667 + 1.312934029 Combine like terms: 0.04166666667 + 1.312934029 = 1.35460069567 1.312934029 + -2.291666667p + p2 = 1.35460069567 Factor a perfect square on the left side: (p + -1.145833334)(p + -1.145833334) = 1.35460069567 Calculate the square root of the right side: 1.163873144 Break this problem into two subproblems by setting (p + -1.145833334) equal to 1.163873144 and -1.163873144.Subproblem 1
p + -1.145833334 = 1.163873144 Simplifying p + -1.145833334 = 1.163873144 Reorder the terms: -1.145833334 + p = 1.163873144 Solving -1.145833334 + p = 1.163873144 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + p = 1.163873144 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + p = 1.163873144 + 1.145833334 p = 1.163873144 + 1.145833334 Combine like terms: 1.163873144 + 1.145833334 = 2.309706478 p = 2.309706478 Simplifying p = 2.309706478Subproblem 2
p + -1.145833334 = -1.163873144 Simplifying p + -1.145833334 = -1.163873144 Reorder the terms: -1.145833334 + p = -1.163873144 Solving -1.145833334 + p = -1.163873144 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + p = -1.163873144 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + p = -1.163873144 + 1.145833334 p = -1.163873144 + 1.145833334 Combine like terms: -1.163873144 + 1.145833334 = -0.01803981 p = -0.01803981 Simplifying p = -0.01803981Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.309706478, -0.01803981}
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