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Simplifying 24x2 + 199x + -81 = 0 Reorder the terms: -81 + 199x + 24x2 = 0 Solving -81 + 199x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -3.375 + 8.291666667x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 8.291666667x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 8.291666667x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 8.291666667x + x2 = 0 + 3.375 8.291666667x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 8.291666667x + x2 = 3.375 The x term is 8.291666667x. Take half its coefficient (4.145833334). Square it (17.18793403) and add it to both sides. Add '17.18793403' to each side of the equation. 8.291666667x + 17.18793403 + x2 = 3.375 + 17.18793403 Reorder the terms: 17.18793403 + 8.291666667x + x2 = 3.375 + 17.18793403 Combine like terms: 3.375 + 17.18793403 = 20.56293403 17.18793403 + 8.291666667x + x2 = 20.56293403 Factor a perfect square on the left side: (x + 4.145833334)(x + 4.145833334) = 20.56293403 Calculate the square root of the right side: 4.534637144 Break this problem into two subproblems by setting (x + 4.145833334) equal to 4.534637144 and -4.534637144.Subproblem 1
x + 4.145833334 = 4.534637144 Simplifying x + 4.145833334 = 4.534637144 Reorder the terms: 4.145833334 + x = 4.534637144 Solving 4.145833334 + x = 4.534637144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.145833334' to each side of the equation. 4.145833334 + -4.145833334 + x = 4.534637144 + -4.145833334 Combine like terms: 4.145833334 + -4.145833334 = 0.000000000 0.000000000 + x = 4.534637144 + -4.145833334 x = 4.534637144 + -4.145833334 Combine like terms: 4.534637144 + -4.145833334 = 0.38880381 x = 0.38880381 Simplifying x = 0.38880381Subproblem 2
x + 4.145833334 = -4.534637144 Simplifying x + 4.145833334 = -4.534637144 Reorder the terms: 4.145833334 + x = -4.534637144 Solving 4.145833334 + x = -4.534637144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.145833334' to each side of the equation. 4.145833334 + -4.145833334 + x = -4.534637144 + -4.145833334 Combine like terms: 4.145833334 + -4.145833334 = 0.000000000 0.000000000 + x = -4.534637144 + -4.145833334 x = -4.534637144 + -4.145833334 Combine like terms: -4.534637144 + -4.145833334 = -8.680470478 x = -8.680470478 Simplifying x = -8.680470478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38880381, -8.680470478}
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