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Simplifying 129 + -197X + -2066(X2) = 50 Solving 129 + -197X + -2066X2 = 50 Solving for variable 'X'. Reorder the terms: 129 + -50 + -197X + -2066X2 = 50 + -50 Combine like terms: 129 + -50 = 79 79 + -197X + -2066X2 = 50 + -50 Combine like terms: 50 + -50 = 0 79 + -197X + -2066X2 = 0 Begin completing the square. Divide all terms by -2066 the coefficient of the squared term: Divide each side by '-2066'. -0.03823814134 + 0.09535333979X + X2 = 0 Move the constant term to the right: Add '0.03823814134' to each side of the equation. -0.03823814134 + 0.09535333979X + 0.03823814134 + X2 = 0 + 0.03823814134 Reorder the terms: -0.03823814134 + 0.03823814134 + 0.09535333979X + X2 = 0 + 0.03823814134 Combine like terms: -0.03823814134 + 0.03823814134 = 0.00000000000 0.00000000000 + 0.09535333979X + X2 = 0 + 0.03823814134 0.09535333979X + X2 = 0 + 0.03823814134 Combine like terms: 0 + 0.03823814134 = 0.03823814134 0.09535333979X + X2 = 0.03823814134 The X term is 0.09535333979X. Take half its coefficient (0.0476766699). Square it (0.002273064853) and add it to both sides. Add '0.002273064853' to each side of the equation. 0.09535333979X + 0.002273064853 + X2 = 0.03823814134 + 0.002273064853 Reorder the terms: 0.002273064853 + 0.09535333979X + X2 = 0.03823814134 + 0.002273064853 Combine like terms: 0.03823814134 + 0.002273064853 = 0.040511206193 0.002273064853 + 0.09535333979X + X2 = 0.040511206193 Factor a perfect square on the left side: (X + 0.0476766699)(X + 0.0476766699) = 0.040511206193 Calculate the square root of the right side: 0.201273958 Break this problem into two subproblems by setting (X + 0.0476766699) equal to 0.201273958 and -0.201273958.Subproblem 1
X + 0.0476766699 = 0.201273958 Simplifying X + 0.0476766699 = 0.201273958 Reorder the terms: 0.0476766699 + X = 0.201273958 Solving 0.0476766699 + X = 0.201273958 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0476766699' to each side of the equation. 0.0476766699 + -0.0476766699 + X = 0.201273958 + -0.0476766699 Combine like terms: 0.0476766699 + -0.0476766699 = 0.0000000000 0.0000000000 + X = 0.201273958 + -0.0476766699 X = 0.201273958 + -0.0476766699 Combine like terms: 0.201273958 + -0.0476766699 = 0.1535972881 X = 0.1535972881 Simplifying X = 0.1535972881Subproblem 2
X + 0.0476766699 = -0.201273958 Simplifying X + 0.0476766699 = -0.201273958 Reorder the terms: 0.0476766699 + X = -0.201273958 Solving 0.0476766699 + X = -0.201273958 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0476766699' to each side of the equation. 0.0476766699 + -0.0476766699 + X = -0.201273958 + -0.0476766699 Combine like terms: 0.0476766699 + -0.0476766699 = 0.0000000000 0.0000000000 + X = -0.201273958 + -0.0476766699 X = -0.201273958 + -0.0476766699 Combine like terms: -0.201273958 + -0.0476766699 = -0.2489506279 X = -0.2489506279 Simplifying X = -0.2489506279Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.1535972881, -0.2489506279}
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