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Simplifying 2x2 + 0.44x + -0.10 = 0 Reorder the terms: -0.10 + 0.44x + 2x2 = 0 Solving -0.10 + 0.44x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.05 + 0.22x + x2 = 0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + 0.22x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + 0.22x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + 0.22x + x2 = 0 + 0.05 0.22x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 0.22x + x2 = 0.05 The x term is 0.22x. Take half its coefficient (0.11). Square it (0.0121) and add it to both sides. Add '0.0121' to each side of the equation. 0.22x + 0.0121 + x2 = 0.05 + 0.0121 Reorder the terms: 0.0121 + 0.22x + x2 = 0.05 + 0.0121 Combine like terms: 0.05 + 0.0121 = 0.0621 0.0121 + 0.22x + x2 = 0.0621 Factor a perfect square on the left side: (x + 0.11)(x + 0.11) = 0.0621 Calculate the square root of the right side: 0.249198716 Break this problem into two subproblems by setting (x + 0.11) equal to 0.249198716 and -0.249198716.Subproblem 1
x + 0.11 = 0.249198716 Simplifying x + 0.11 = 0.249198716 Reorder the terms: 0.11 + x = 0.249198716 Solving 0.11 + x = 0.249198716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.11' to each side of the equation. 0.11 + -0.11 + x = 0.249198716 + -0.11 Combine like terms: 0.11 + -0.11 = 0.00 0.00 + x = 0.249198716 + -0.11 x = 0.249198716 + -0.11 Combine like terms: 0.249198716 + -0.11 = 0.139198716 x = 0.139198716 Simplifying x = 0.139198716Subproblem 2
x + 0.11 = -0.249198716 Simplifying x + 0.11 = -0.249198716 Reorder the terms: 0.11 + x = -0.249198716 Solving 0.11 + x = -0.249198716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.11' to each side of the equation. 0.11 + -0.11 + x = -0.249198716 + -0.11 Combine like terms: 0.11 + -0.11 = 0.00 0.00 + x = -0.249198716 + -0.11 x = -0.249198716 + -0.11 Combine like terms: -0.249198716 + -0.11 = -0.359198716 x = -0.359198716 Simplifying x = -0.359198716Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.139198716, -0.359198716}
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