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Simplifying -3.5x2 + 0.5x + 1 = 0 Reorder the terms: 1 + 0.5x + -3.5x2 = 0 Solving 1 + 0.5x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -0.2857142857 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.1428571429x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.1428571429x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + 0.2857142857 -0.1428571429x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.1428571429x + x2 = 0.2857142857 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.2857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.2857142857 + 0.005102040819 Combine like terms: 0.2857142857 + 0.005102040819 = 0.290816326519 0.005102040819 + -0.1428571429x + x2 = 0.290816326519 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.290816326519 Calculate the square root of the right side: 0.539273888 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.539273888 and -0.539273888.Subproblem 1
x + -0.07142857145 = 0.539273888 Simplifying x + -0.07142857145 = 0.539273888 Reorder the terms: -0.07142857145 + x = 0.539273888 Solving -0.07142857145 + x = 0.539273888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.539273888 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.539273888 + 0.07142857145 x = 0.539273888 + 0.07142857145 Combine like terms: 0.539273888 + 0.07142857145 = 0.61070245945 x = 0.61070245945 Simplifying x = 0.61070245945Subproblem 2
x + -0.07142857145 = -0.539273888 Simplifying x + -0.07142857145 = -0.539273888 Reorder the terms: -0.07142857145 + x = -0.539273888 Solving -0.07142857145 + x = -0.539273888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.539273888 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.539273888 + 0.07142857145 x = -0.539273888 + 0.07142857145 Combine like terms: -0.539273888 + 0.07142857145 = -0.46784531655 x = -0.46784531655 Simplifying x = -0.46784531655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.61070245945, -0.46784531655}
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