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Simplifying 2.1x2 + -6.2x + 3.1 = 0 Reorder the terms: 3.1 + -6.2x + 2.1x2 = 0 Solving 3.1 + -6.2x + 2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.1 the coefficient of the squared term: Divide each side by '2.1'. 1.476190476 + -2.952380952x + x2 = 0 Move the constant term to the right: Add '-1.476190476' to each side of the equation. 1.476190476 + -2.952380952x + -1.476190476 + x2 = 0 + -1.476190476 Reorder the terms: 1.476190476 + -1.476190476 + -2.952380952x + x2 = 0 + -1.476190476 Combine like terms: 1.476190476 + -1.476190476 = 0.000000000 0.000000000 + -2.952380952x + x2 = 0 + -1.476190476 -2.952380952x + x2 = 0 + -1.476190476 Combine like terms: 0 + -1.476190476 = -1.476190476 -2.952380952x + x2 = -1.476190476 The x term is -2.952380952x. Take half its coefficient (-1.476190476). Square it (2.179138321) and add it to both sides. Add '2.179138321' to each side of the equation. -2.952380952x + 2.179138321 + x2 = -1.476190476 + 2.179138321 Reorder the terms: 2.179138321 + -2.952380952x + x2 = -1.476190476 + 2.179138321 Combine like terms: -1.476190476 + 2.179138321 = 0.702947845 2.179138321 + -2.952380952x + x2 = 0.702947845 Factor a perfect square on the left side: (x + -1.476190476)(x + -1.476190476) = 0.702947845 Calculate the square root of the right side: 0.83841985 Break this problem into two subproblems by setting (x + -1.476190476) equal to 0.83841985 and -0.83841985.Subproblem 1
x + -1.476190476 = 0.83841985 Simplifying x + -1.476190476 = 0.83841985 Reorder the terms: -1.476190476 + x = 0.83841985 Solving -1.476190476 + x = 0.83841985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.476190476' to each side of the equation. -1.476190476 + 1.476190476 + x = 0.83841985 + 1.476190476 Combine like terms: -1.476190476 + 1.476190476 = 0.000000000 0.000000000 + x = 0.83841985 + 1.476190476 x = 0.83841985 + 1.476190476 Combine like terms: 0.83841985 + 1.476190476 = 2.314610326 x = 2.314610326 Simplifying x = 2.314610326Subproblem 2
x + -1.476190476 = -0.83841985 Simplifying x + -1.476190476 = -0.83841985 Reorder the terms: -1.476190476 + x = -0.83841985 Solving -1.476190476 + x = -0.83841985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.476190476' to each side of the equation. -1.476190476 + 1.476190476 + x = -0.83841985 + 1.476190476 Combine like terms: -1.476190476 + 1.476190476 = 0.000000000 0.000000000 + x = -0.83841985 + 1.476190476 x = -0.83841985 + 1.476190476 Combine like terms: -0.83841985 + 1.476190476 = 0.637770626 x = 0.637770626 Simplifying x = 0.637770626Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.314610326, 0.637770626}
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