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Simplifying 4.9x2 + -6x + -2 = 0 Reorder the terms: -2 + -6x + 4.9x2 = 0 Solving -2 + -6x + 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'. -0.4081632653 + -1.224489796x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -1.224489796x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -1.224489796x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -1.224489796x + x2 = 0 + 0.4081632653 -1.224489796x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -1.224489796x + x2 = 0.4081632653 The x term is -1.224489796x. Take half its coefficient (-0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. -1.224489796x + 0.3748438151 + x2 = 0.4081632653 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796x + x2 = 0.4081632653 + 0.3748438151 Combine like terms: 0.4081632653 + 0.3748438151 = 0.7830070804 0.3748438151 + -1.224489796x + x2 = 0.7830070804 Factor a perfect square on the left side: (x + -0.612244898)(x + -0.612244898) = 0.7830070804 Calculate the square root of the right side: 0.884876873 Break this problem into two subproblems by setting (x + -0.612244898) equal to 0.884876873 and -0.884876873.Subproblem 1
x + -0.612244898 = 0.884876873 Simplifying x + -0.612244898 = 0.884876873 Reorder the terms: -0.612244898 + x = 0.884876873 Solving -0.612244898 + x = 0.884876873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + x = 0.884876873 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = 0.884876873 + 0.612244898 x = 0.884876873 + 0.612244898 Combine like terms: 0.884876873 + 0.612244898 = 1.497121771 x = 1.497121771 Simplifying x = 1.497121771Subproblem 2
x + -0.612244898 = -0.884876873 Simplifying x + -0.612244898 = -0.884876873 Reorder the terms: -0.612244898 + x = -0.884876873 Solving -0.612244898 + x = -0.884876873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + x = -0.884876873 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = -0.884876873 + 0.612244898 x = -0.884876873 + 0.612244898 Combine like terms: -0.884876873 + 0.612244898 = -0.272631975 x = -0.272631975 Simplifying x = -0.272631975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.497121771, -0.272631975}
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