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Simplifying 6x2 + 7x = 12 Reorder the terms: 7x + 6x2 = 12 Solving 7x + 6x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 7x + 6x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.166666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.166666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.166666667x + x2 = 0 + 2 1.166666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.166666667x + x2 = 2 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 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 2 + 0.3402777780 Combine like terms: 2 + 0.3402777780 = 2.340277778 0.3402777780 + 1.166666667x + x2 = 2.340277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 2.340277778 Calculate the square root of the right side: 1.529796646 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.529796646 and -1.529796646.Subproblem 1
x + 0.5833333335 = 1.529796646 Simplifying x + 0.5833333335 = 1.529796646 Reorder the terms: 0.5833333335 + x = 1.529796646 Solving 0.5833333335 + x = 1.529796646 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 = 1.529796646 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.529796646 + -0.5833333335 x = 1.529796646 + -0.5833333335 Combine like terms: 1.529796646 + -0.5833333335 = 0.9464633125 x = 0.9464633125 Simplifying x = 0.9464633125Subproblem 2
x + 0.5833333335 = -1.529796646 Simplifying x + 0.5833333335 = -1.529796646 Reorder the terms: 0.5833333335 + x = -1.529796646 Solving 0.5833333335 + x = -1.529796646 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 = -1.529796646 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.529796646 + -0.5833333335 x = -1.529796646 + -0.5833333335 Combine like terms: -1.529796646 + -0.5833333335 = -2.1131299795 x = -2.1131299795 Simplifying x = -2.1131299795Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9464633125, -2.1131299795}
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