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Simplifying 0.204 = 2(x) + 4.9(x2) Solving 0.204 = 2x + 4.9x2 Solving for variable 'x'. Reorder the terms: 0.204 + -2x + -4.9x2 = 2x + -2x + 4.9x2 + -4.9x2 Combine like terms: 2x + -2x = 0 0.204 + -2x + -4.9x2 = 0 + 4.9x2 + -4.9x2 0.204 + -2x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 0.204 + -2x + -4.9x2 = 0.0 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 = 0.08328196587 0.04164931281 + 0.4081632653x + x2 = 0.08328196587 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 0.08328196587 Calculate the square root of the right side: 0.28858615 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 0.28858615 and -0.28858615.Subproblem 1
x + 0.2040816327 = 0.28858615 Simplifying x + 0.2040816327 = 0.28858615 Reorder the terms: 0.2040816327 + x = 0.28858615 Solving 0.2040816327 + x = 0.28858615 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 = 0.28858615 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 0.28858615 + -0.2040816327 x = 0.28858615 + -0.2040816327 Combine like terms: 0.28858615 + -0.2040816327 = 0.0845045173 x = 0.0845045173 Simplifying x = 0.0845045173Subproblem 2
x + 0.2040816327 = -0.28858615 Simplifying x + 0.2040816327 = -0.28858615 Reorder the terms: 0.2040816327 + x = -0.28858615 Solving 0.2040816327 + x = -0.28858615 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 = -0.28858615 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -0.28858615 + -0.2040816327 x = -0.28858615 + -0.2040816327 Combine like terms: -0.28858615 + -0.2040816327 = -0.4926677827 x = -0.4926677827 Simplifying x = -0.4926677827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0845045173, -0.4926677827}
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