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Simplifying 6x2 + 8 = -55x Reorder the terms: 8 + 6x2 = -55x Solving 8 + 6x2 = -55x Solving for variable 'x'. Reorder the terms: 8 + 55x + 6x2 = -55x + 55x Combine like terms: -55x + 55x = 0 8 + 55x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + 9.166666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 9.166666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 9.166666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 9.166666667x + x2 = 0 + -1.333333333 9.166666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 9.166666667x + x2 = -1.333333333 The x term is 9.166666667x. Take half its coefficient (4.583333334). Square it (21.00694445) and add it to both sides. Add '21.00694445' to each side of the equation. 9.166666667x + 21.00694445 + x2 = -1.333333333 + 21.00694445 Reorder the terms: 21.00694445 + 9.166666667x + x2 = -1.333333333 + 21.00694445 Combine like terms: -1.333333333 + 21.00694445 = 19.673611117 21.00694445 + 9.166666667x + x2 = 19.673611117 Factor a perfect square on the left side: (x + 4.583333334)(x + 4.583333334) = 19.673611117 Calculate the square root of the right side: 4.435494461 Break this problem into two subproblems by setting (x + 4.583333334) equal to 4.435494461 and -4.435494461.Subproblem 1
x + 4.583333334 = 4.435494461 Simplifying x + 4.583333334 = 4.435494461 Reorder the terms: 4.583333334 + x = 4.435494461 Solving 4.583333334 + x = 4.435494461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.583333334' to each side of the equation. 4.583333334 + -4.583333334 + x = 4.435494461 + -4.583333334 Combine like terms: 4.583333334 + -4.583333334 = 0.000000000 0.000000000 + x = 4.435494461 + -4.583333334 x = 4.435494461 + -4.583333334 Combine like terms: 4.435494461 + -4.583333334 = -0.147838873 x = -0.147838873 Simplifying x = -0.147838873Subproblem 2
x + 4.583333334 = -4.435494461 Simplifying x + 4.583333334 = -4.435494461 Reorder the terms: 4.583333334 + x = -4.435494461 Solving 4.583333334 + x = -4.435494461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.583333334' to each side of the equation. 4.583333334 + -4.583333334 + x = -4.435494461 + -4.583333334 Combine like terms: 4.583333334 + -4.583333334 = 0.000000000 0.000000000 + x = -4.435494461 + -4.583333334 x = -4.435494461 + -4.583333334 Combine like terms: -4.435494461 + -4.583333334 = -9.018827795 x = -9.018827795 Simplifying x = -9.018827795Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.147838873, -9.018827795}
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