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Simplifying -4.9x2 + 2x + -0.204 = 0 Reorder the terms: -0.204 + 2x + -4.9x2 = 0 Solving -0.204 + 2x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.04163265306 + -0.4081632653x + x2 = 0 Move the constant term to the right: Add '-0.04163265306' to each side of the equation. 0.04163265306 + -0.4081632653x + -0.04163265306 + x2 = 0 + -0.04163265306 Reorder the terms: 0.04163265306 + -0.04163265306 + -0.4081632653x + x2 = 0 + -0.04163265306 Combine like terms: 0.04163265306 + -0.04163265306 = 0.00000000000 0.00000000000 + -0.4081632653x + x2 = 0 + -0.04163265306 -0.4081632653x + x2 = 0 + -0.04163265306 Combine like terms: 0 + -0.04163265306 = -0.04163265306 -0.4081632653x + x2 = -0.04163265306 The x term is -0.4081632653x. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653x + 0.04164931281 + x2 = -0.04163265306 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653x + x2 = -0.04163265306 + 0.04164931281 Combine like terms: -0.04163265306 + 0.04164931281 = 0.00001665975 0.04164931281 + -0.4081632653x + x2 = 0.00001665975 Factor a perfect square on the left side: (x + -0.2040816327)(x + -0.2040816327) = 0.00001665975 Calculate the square root of the right side: 0.004081636 Break this problem into two subproblems by setting (x + -0.2040816327) equal to 0.004081636 and -0.004081636.Subproblem 1
x + -0.2040816327 = 0.004081636 Simplifying x + -0.2040816327 = 0.004081636 Reorder the terms: -0.2040816327 + x = 0.004081636 Solving -0.2040816327 + x = 0.004081636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + x = 0.004081636 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + x = 0.004081636 + 0.2040816327 x = 0.004081636 + 0.2040816327 Combine like terms: 0.004081636 + 0.2040816327 = 0.2081632687 x = 0.2081632687 Simplifying x = 0.2081632687Subproblem 2
x + -0.2040816327 = -0.004081636 Simplifying x + -0.2040816327 = -0.004081636 Reorder the terms: -0.2040816327 + x = -0.004081636 Solving -0.2040816327 + x = -0.004081636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + x = -0.004081636 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + x = -0.004081636 + 0.2040816327 x = -0.004081636 + 0.2040816327 Combine like terms: -0.004081636 + 0.2040816327 = 0.1999999967 x = 0.1999999967 Simplifying x = 0.1999999967Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2081632687, 0.1999999967}
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