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Simplifying 2.3x2 + 3.5x + -1.2 = 0 Reorder the terms: -1.2 + 3.5x + 2.3x2 = 0 Solving -1.2 + 3.5x + 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'. -0.5217391304 + 1.52173913x + x2 = 0 Move the constant term to the right: Add '0.5217391304' to each side of the equation. -0.5217391304 + 1.52173913x + 0.5217391304 + x2 = 0 + 0.5217391304 Reorder the terms: -0.5217391304 + 0.5217391304 + 1.52173913x + x2 = 0 + 0.5217391304 Combine like terms: -0.5217391304 + 0.5217391304 = 0.0000000000 0.0000000000 + 1.52173913x + x2 = 0 + 0.5217391304 1.52173913x + x2 = 0 + 0.5217391304 Combine like terms: 0 + 0.5217391304 = 0.5217391304 1.52173913x + x2 = 0.5217391304 The x term is 1.52173913x. Take half its coefficient (0.760869565). Square it (0.5789224949) and add it to both sides. Add '0.5789224949' to each side of the equation. 1.52173913x + 0.5789224949 + x2 = 0.5217391304 + 0.5789224949 Reorder the terms: 0.5789224949 + 1.52173913x + x2 = 0.5217391304 + 0.5789224949 Combine like terms: 0.5217391304 + 0.5789224949 = 1.1006616253 0.5789224949 + 1.52173913x + x2 = 1.1006616253 Factor a perfect square on the left side: (x + 0.760869565)(x + 0.760869565) = 1.1006616253 Calculate the square root of the right side: 1.049124218 Break this problem into two subproblems by setting (x + 0.760869565) equal to 1.049124218 and -1.049124218.Subproblem 1
x + 0.760869565 = 1.049124218 Simplifying x + 0.760869565 = 1.049124218 Reorder the terms: 0.760869565 + x = 1.049124218 Solving 0.760869565 + x = 1.049124218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.760869565' to each side of the equation. 0.760869565 + -0.760869565 + x = 1.049124218 + -0.760869565 Combine like terms: 0.760869565 + -0.760869565 = 0.000000000 0.000000000 + x = 1.049124218 + -0.760869565 x = 1.049124218 + -0.760869565 Combine like terms: 1.049124218 + -0.760869565 = 0.288254653 x = 0.288254653 Simplifying x = 0.288254653Subproblem 2
x + 0.760869565 = -1.049124218 Simplifying x + 0.760869565 = -1.049124218 Reorder the terms: 0.760869565 + x = -1.049124218 Solving 0.760869565 + x = -1.049124218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.760869565' to each side of the equation. 0.760869565 + -0.760869565 + x = -1.049124218 + -0.760869565 Combine like terms: 0.760869565 + -0.760869565 = 0.000000000 0.000000000 + x = -1.049124218 + -0.760869565 x = -1.049124218 + -0.760869565 Combine like terms: -1.049124218 + -0.760869565 = -1.809993783 x = -1.809993783 Simplifying x = -1.809993783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288254653, -1.809993783}
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