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Simplifying 2.3x2 + -1.4x + -6.8 = 0 Reorder the terms: -6.8 + -1.4x + 2.3x2 = 0 Solving -6.8 + -1.4x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -2.956521739 + -0.6086956522x + x2 = 0 Move the constant term to the right: Add '2.956521739' to each side of the equation. -2.956521739 + -0.6086956522x + 2.956521739 + x2 = 0 + 2.956521739 Reorder the terms: -2.956521739 + 2.956521739 + -0.6086956522x + x2 = 0 + 2.956521739 Combine like terms: -2.956521739 + 2.956521739 = 0.000000000 0.000000000 + -0.6086956522x + x2 = 0 + 2.956521739 -0.6086956522x + x2 = 0 + 2.956521739 Combine like terms: 0 + 2.956521739 = 2.956521739 -0.6086956522x + x2 = 2.956521739 The x term is -0.6086956522x. Take half its coefficient (-0.3043478261). Square it (0.09262759925) and add it to both sides. Add '0.09262759925' to each side of the equation. -0.6086956522x + 0.09262759925 + x2 = 2.956521739 + 0.09262759925 Reorder the terms: 0.09262759925 + -0.6086956522x + x2 = 2.956521739 + 0.09262759925 Combine like terms: 2.956521739 + 0.09262759925 = 3.04914933825 0.09262759925 + -0.6086956522x + x2 = 3.04914933825 Factor a perfect square on the left side: (x + -0.3043478261)(x + -0.3043478261) = 3.04914933825 Calculate the square root of the right side: 1.746181359 Break this problem into two subproblems by setting (x + -0.3043478261) equal to 1.746181359 and -1.746181359.Subproblem 1
x + -0.3043478261 = 1.746181359 Simplifying x + -0.3043478261 = 1.746181359 Reorder the terms: -0.3043478261 + x = 1.746181359 Solving -0.3043478261 + x = 1.746181359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3043478261' to each side of the equation. -0.3043478261 + 0.3043478261 + x = 1.746181359 + 0.3043478261 Combine like terms: -0.3043478261 + 0.3043478261 = 0.0000000000 0.0000000000 + x = 1.746181359 + 0.3043478261 x = 1.746181359 + 0.3043478261 Combine like terms: 1.746181359 + 0.3043478261 = 2.0505291851 x = 2.0505291851 Simplifying x = 2.0505291851Subproblem 2
x + -0.3043478261 = -1.746181359 Simplifying x + -0.3043478261 = -1.746181359 Reorder the terms: -0.3043478261 + x = -1.746181359 Solving -0.3043478261 + x = -1.746181359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3043478261' to each side of the equation. -0.3043478261 + 0.3043478261 + x = -1.746181359 + 0.3043478261 Combine like terms: -0.3043478261 + 0.3043478261 = 0.0000000000 0.0000000000 + x = -1.746181359 + 0.3043478261 x = -1.746181359 + 0.3043478261 Combine like terms: -1.746181359 + 0.3043478261 = -1.4418335329 x = -1.4418335329 Simplifying x = -1.4418335329Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0505291851, -1.4418335329}
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