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Simplifying -3.25x2 + -6x + 76 = 0 Reorder the terms: 76 + -6x + -3.25x2 = 0 Solving 76 + -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'. -23.38461538 + 1.846153846x + x2 = 0 Move the constant term to the right: Add '23.38461538' to each side of the equation. -23.38461538 + 1.846153846x + 23.38461538 + x2 = 0 + 23.38461538 Reorder the terms: -23.38461538 + 23.38461538 + 1.846153846x + x2 = 0 + 23.38461538 Combine like terms: -23.38461538 + 23.38461538 = 0.00000000 0.00000000 + 1.846153846x + x2 = 0 + 23.38461538 1.846153846x + x2 = 0 + 23.38461538 Combine like terms: 0 + 23.38461538 = 23.38461538 1.846153846x + x2 = 23.38461538 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 = 23.38461538 + 0.8520710058 Reorder the terms: 0.8520710058 + 1.846153846x + x2 = 23.38461538 + 0.8520710058 Combine like terms: 23.38461538 + 0.8520710058 = 24.2366863858 0.8520710058 + 1.846153846x + x2 = 24.2366863858 Factor a perfect square on the left side: (x + 0.923076923)(x + 0.923076923) = 24.2366863858 Calculate the square root of the right side: 4.923076923 Break this problem into two subproblems by setting (x + 0.923076923) equal to 4.923076923 and -4.923076923.Subproblem 1
x + 0.923076923 = 4.923076923 Simplifying x + 0.923076923 = 4.923076923 Reorder the terms: 0.923076923 + x = 4.923076923 Solving 0.923076923 + x = 4.923076923 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 = 4.923076923 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = 4.923076923 + -0.923076923 x = 4.923076923 + -0.923076923 Combine like terms: 4.923076923 + -0.923076923 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 0.923076923 = -4.923076923 Simplifying x + 0.923076923 = -4.923076923 Reorder the terms: 0.923076923 + x = -4.923076923 Solving 0.923076923 + x = -4.923076923 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 = -4.923076923 + -0.923076923 Combine like terms: 0.923076923 + -0.923076923 = 0.000000000 0.000000000 + x = -4.923076923 + -0.923076923 x = -4.923076923 + -0.923076923 Combine like terms: -4.923076923 + -0.923076923 = -5.846153846 x = -5.846153846 Simplifying x = -5.846153846Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -5.846153846}
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