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Simplifying 50x2 + -20x + 1.5 = 4x2 Reorder the terms: 1.5 + -20x + 50x2 = 4x2 Solving 1.5 + -20x + 50x2 = 4x2 Solving for variable 'x'. Combine like terms: 50x2 + -4x2 = 46x2 1.5 + -20x + 46x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1.5 + -20x + 46x2 = 0 Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. 0.03260869565 + -0.4347826087x + x2 = 0 Move the constant term to the right: Add '-0.03260869565' to each side of the equation. 0.03260869565 + -0.4347826087x + -0.03260869565 + x2 = 0 + -0.03260869565 Reorder the terms: 0.03260869565 + -0.03260869565 + -0.4347826087x + x2 = 0 + -0.03260869565 Combine like terms: 0.03260869565 + -0.03260869565 = 0.00000000000 0.00000000000 + -0.4347826087x + x2 = 0 + -0.03260869565 -0.4347826087x + x2 = 0 + -0.03260869565 Combine like terms: 0 + -0.03260869565 = -0.03260869565 -0.4347826087x + x2 = -0.03260869565 The x term is -0.4347826087x. Take half its coefficient (-0.2173913044). Square it (0.04725897923) and add it to both sides. Add '0.04725897923' to each side of the equation. -0.4347826087x + 0.04725897923 + x2 = -0.03260869565 + 0.04725897923 Reorder the terms: 0.04725897923 + -0.4347826087x + x2 = -0.03260869565 + 0.04725897923 Combine like terms: -0.03260869565 + 0.04725897923 = 0.01465028358 0.04725897923 + -0.4347826087x + x2 = 0.01465028358 Factor a perfect square on the left side: (x + -0.2173913044)(x + -0.2173913044) = 0.01465028358 Calculate the square root of the right side: 0.121038356 Break this problem into two subproblems by setting (x + -0.2173913044) equal to 0.121038356 and -0.121038356.Subproblem 1
x + -0.2173913044 = 0.121038356 Simplifying x + -0.2173913044 = 0.121038356 Reorder the terms: -0.2173913044 + x = 0.121038356 Solving -0.2173913044 + x = 0.121038356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = 0.121038356 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = 0.121038356 + 0.2173913044 x = 0.121038356 + 0.2173913044 Combine like terms: 0.121038356 + 0.2173913044 = 0.3384296604 x = 0.3384296604 Simplifying x = 0.3384296604Subproblem 2
x + -0.2173913044 = -0.121038356 Simplifying x + -0.2173913044 = -0.121038356 Reorder the terms: -0.2173913044 + x = -0.121038356 Solving -0.2173913044 + x = -0.121038356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = -0.121038356 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = -0.121038356 + 0.2173913044 x = -0.121038356 + 0.2173913044 Combine like terms: -0.121038356 + 0.2173913044 = 0.0963529484 x = 0.0963529484 Simplifying x = 0.0963529484Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3384296604, 0.0963529484}
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