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Simplifying 12x2 + -14x + 3 = 0 Reorder the terms: 3 + -14x + 12x2 = 0 Solving 3 + -14x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.166666667x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.166666667x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.166666667x + x2 = 0 + -0.25 -1.166666667x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.166666667x + x2 = -0.25 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = -0.25 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -0.25 + 0.3402777780 Combine like terms: -0.25 + 0.3402777780 = 0.090277778 0.3402777780 + -1.166666667x + x2 = 0.090277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.090277778 Calculate the square root of the right side: 0.300462607 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.300462607 and -0.300462607.Subproblem 1
x + -0.5833333335 = 0.300462607 Simplifying x + -0.5833333335 = 0.300462607 Reorder the terms: -0.5833333335 + x = 0.300462607 Solving -0.5833333335 + x = 0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 0.300462607 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.300462607 + 0.5833333335 x = 0.300462607 + 0.5833333335 Combine like terms: 0.300462607 + 0.5833333335 = 0.8837959405 x = 0.8837959405 Simplifying x = 0.8837959405Subproblem 2
x + -0.5833333335 = -0.300462607 Simplifying x + -0.5833333335 = -0.300462607 Reorder the terms: -0.5833333335 + x = -0.300462607 Solving -0.5833333335 + x = -0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -0.300462607 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.300462607 + 0.5833333335 x = -0.300462607 + 0.5833333335 Combine like terms: -0.300462607 + 0.5833333335 = 0.2828707265 x = 0.2828707265 Simplifying x = 0.2828707265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8837959405, 0.2828707265}
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