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Simplifying 20x + 114 = 46x2 Reorder the terms: 114 + 20x = 46x2 Solving 114 + 20x = 46x2 Solving for variable 'x'. Combine like terms: 46x2 + -46x2 = 0 114 + 20x + -46x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + 10x + -23x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(57 + 10x + -23x2)' equal to zero and attempt to solve: Simplifying 57 + 10x + -23x2 = 0 Solving 57 + 10x + -23x2 = 0 Begin completing the square. Divide all terms by -23 the coefficient of the squared term: Divide each side by '-23'. -2.47826087 + -0.4347826087x + x2 = 0 Move the constant term to the right: Add '2.47826087' to each side of the equation. -2.47826087 + -0.4347826087x + 2.47826087 + x2 = 0 + 2.47826087 Reorder the terms: -2.47826087 + 2.47826087 + -0.4347826087x + x2 = 0 + 2.47826087 Combine like terms: -2.47826087 + 2.47826087 = 0.00000000 0.00000000 + -0.4347826087x + x2 = 0 + 2.47826087 -0.4347826087x + x2 = 0 + 2.47826087 Combine like terms: 0 + 2.47826087 = 2.47826087 -0.4347826087x + x2 = 2.47826087 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 = 2.47826087 + 0.04725897923 Reorder the terms: 0.04725897923 + -0.4347826087x + x2 = 2.47826087 + 0.04725897923 Combine like terms: 2.47826087 + 0.04725897923 = 2.52551984923 0.04725897923 + -0.4347826087x + x2 = 2.52551984923 Factor a perfect square on the left side: (x + -0.2173913044)(x + -0.2173913044) = 2.52551984923 Calculate the square root of the right side: 1.589188425 Break this problem into two subproblems by setting (x + -0.2173913044) equal to 1.589188425 and -1.589188425.Subproblem 1
x + -0.2173913044 = 1.589188425 Simplifying x + -0.2173913044 = 1.589188425 Reorder the terms: -0.2173913044 + x = 1.589188425 Solving -0.2173913044 + x = 1.589188425 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 = 1.589188425 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = 1.589188425 + 0.2173913044 x = 1.589188425 + 0.2173913044 Combine like terms: 1.589188425 + 0.2173913044 = 1.8065797294 x = 1.8065797294 Simplifying x = 1.8065797294Subproblem 2
x + -0.2173913044 = -1.589188425 Simplifying x + -0.2173913044 = -1.589188425 Reorder the terms: -0.2173913044 + x = -1.589188425 Solving -0.2173913044 + x = -1.589188425 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 = -1.589188425 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = -1.589188425 + 0.2173913044 x = -1.589188425 + 0.2173913044 Combine like terms: -1.589188425 + 0.2173913044 = -1.3717971206 x = -1.3717971206 Simplifying x = -1.3717971206Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8065797294, -1.3717971206}Solution
x = {1.8065797294, -1.3717971206}
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