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Simplifying 2x2 + -6x + 4.408 = 0 Reorder the terms: 4.408 + -6x + 2x2 = 0 Solving 4.408 + -6x + 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'. 2.204 + -3x + x2 = 0 Move the constant term to the right: Add '-2.204' to each side of the equation. 2.204 + -3x + -2.204 + x2 = 0 + -2.204 Reorder the terms: 2.204 + -2.204 + -3x + x2 = 0 + -2.204 Combine like terms: 2.204 + -2.204 = 0.000 0.000 + -3x + x2 = 0 + -2.204 -3x + x2 = 0 + -2.204 Combine like terms: 0 + -2.204 = -2.204 -3x + x2 = -2.204 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.204 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.204 + 2.25 Combine like terms: -2.204 + 2.25 = 0.046 2.25 + -3x + x2 = 0.046 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.046 Calculate the square root of the right side: 0.214476106 Break this problem into two subproblems by setting (x + -1.5) equal to 0.214476106 and -0.214476106.Subproblem 1
x + -1.5 = 0.214476106 Simplifying x + -1.5 = 0.214476106 Reorder the terms: -1.5 + x = 0.214476106 Solving -1.5 + x = 0.214476106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.214476106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.214476106 + 1.5 x = 0.214476106 + 1.5 Combine like terms: 0.214476106 + 1.5 = 1.714476106 x = 1.714476106 Simplifying x = 1.714476106Subproblem 2
x + -1.5 = -0.214476106 Simplifying x + -1.5 = -0.214476106 Reorder the terms: -1.5 + x = -0.214476106 Solving -1.5 + x = -0.214476106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.214476106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.214476106 + 1.5 x = -0.214476106 + 1.5 Combine like terms: -0.214476106 + 1.5 = 1.285523894 x = 1.285523894 Simplifying x = 1.285523894Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.714476106, 1.285523894}
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