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Simplifying 86 + -6x + -3x2 + -0.25x2 + 10 = 0 Reorder the terms: 86 + 10 + -6x + -3x2 + -0.25x2 = 0 Combine like terms: 86 + 10 = 96 96 + -6x + -3x2 + -0.25x2 = 0 Combine like terms: -3x2 + -0.25x2 = -3.25x2 96 + -6x + -3.25x2 = 0 Solving 96 + -6x + -3.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.25 the coefficient of the squared term: Divide each side by '-3.25'. -29.53846154 + 1.846153846x + x2 = 0 Move the constant term to the right: Add '29.53846154' to each side of the equation. -29.53846154 + 1.846153846x + 29.53846154 + x2 = 0 + 29.53846154 Reorder the terms: -29.53846154 + 29.53846154 + 1.846153846x + x2 = 0 + 29.53846154 Combine like terms: -29.53846154 + 29.53846154 = 0.00000000 0.00000000 + 1.846153846x + x2 = 0 + 29.53846154 1.846153846x + x2 = 0 + 29.53846154 Combine like terms: 0 + 29.53846154 = 29.53846154 1.846153846x + x2 = 29.53846154 The x term is 1.846153846x. Take half its coefficient (0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. 1.846153846x + 0.8520710058 + x2 = 29.53846154 + 0.8520710058 Reorder the terms: 0.8520710058 + 1.846153846x + x2 = 29.53846154 + 0.8520710058 Combine like terms: 29.53846154 + 0.8520710058 = 30.3905325458 0.8520710058 + 1.846153846x + x2 = 30.3905325458 Factor a perfect square on the left side: (x + 0.923076923)(x + 0.923076923) = 30.3905325458 Calculate the square root of the right side: 5.512760882 Break this problem into two subproblems by setting (x + 0.923076923) equal to 5.512760882 and -5.512760882.Subproblem 1
x + 0.923076923 = 5.512760882 Simplifying x + 0.923076923 = 5.512760882 Reorder the terms: 0.923076923 + x = 5.512760882 Solving 0.923076923 + x = 5.512760882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + x = 5.512760882 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = 5.512760882 + -0.923076923 x = 5.512760882 + -0.923076923 Combine like terms: 5.512760882 + -0.923076923 = 4.589683959 x = 4.589683959 Simplifying x = 4.589683959Subproblem 2
x + 0.923076923 = -5.512760882 Simplifying x + 0.923076923 = -5.512760882 Reorder the terms: 0.923076923 + x = -5.512760882 Solving 0.923076923 + x = -5.512760882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.923076923' to each side of the equation. 0.923076923 + -0.923076923 + x = -5.512760882 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = -5.512760882 + -0.923076923 x = -5.512760882 + -0.923076923 Combine like terms: -5.512760882 + -0.923076923 = -6.435837805 x = -6.435837805 Simplifying x = -6.435837805Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.589683959, -6.435837805}
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