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Simplifying 6x2 + 7x + -14 = 0 Reorder the terms: -14 + 7x + 6x2 = 0 Solving -14 + 7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.333333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 1.166666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 1.166666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 2.333333333 1.166666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 1.166666667x + x2 = 2.333333333 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 = 2.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 2.333333333 + 0.3402777780 Combine like terms: 2.333333333 + 0.3402777780 = 2.673611111 0.3402777780 + 1.166666667x + x2 = 2.673611111 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 2.673611111 Calculate the square root of the right side: 1.635118072 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.635118072 and -1.635118072.Subproblem 1
x + 0.5833333335 = 1.635118072 Simplifying x + 0.5833333335 = 1.635118072 Reorder the terms: 0.5833333335 + x = 1.635118072 Solving 0.5833333335 + x = 1.635118072 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 = 1.635118072 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.635118072 + -0.5833333335 x = 1.635118072 + -0.5833333335 Combine like terms: 1.635118072 + -0.5833333335 = 1.0517847385 x = 1.0517847385 Simplifying x = 1.0517847385Subproblem 2
x + 0.5833333335 = -1.635118072 Simplifying x + 0.5833333335 = -1.635118072 Reorder the terms: 0.5833333335 + x = -1.635118072 Solving 0.5833333335 + x = -1.635118072 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 = -1.635118072 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.635118072 + -0.5833333335 x = -1.635118072 + -0.5833333335 Combine like terms: -1.635118072 + -0.5833333335 = -2.2184514055 x = -2.2184514055 Simplifying x = -2.2184514055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0517847385, -2.2184514055}
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