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Simplifying 6x2 + 7x = 2 Reorder the terms: 7x + 6x2 = 2 Solving 7x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 7x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.166666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.166666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + 0.3333333333 1.166666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.166666667x + x2 = 0.3333333333 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 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + 1.166666667x + x2 = 0.6736111113 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
x + 0.5833333335 = 0.82073815 Simplifying x + 0.5833333335 = 0.82073815 Reorder the terms: 0.5833333335 + x = 0.82073815 Solving 0.5833333335 + x = 0.82073815 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 = 0.82073815 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.82073815 + -0.5833333335 x = 0.82073815 + -0.5833333335 Combine like terms: 0.82073815 + -0.5833333335 = 0.2374048165 x = 0.2374048165 Simplifying x = 0.2374048165Subproblem 2
x + 0.5833333335 = -0.82073815 Simplifying x + 0.5833333335 = -0.82073815 Reorder the terms: 0.5833333335 + x = -0.82073815 Solving 0.5833333335 + x = -0.82073815 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 = -0.82073815 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.82073815 + -0.5833333335 x = -0.82073815 + -0.5833333335 Combine like terms: -0.82073815 + -0.5833333335 = -1.4040714835 x = -1.4040714835 Simplifying x = -1.4040714835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2374048165, -1.4040714835}
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