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Simplifying 6x2 = 7x + 8 Reorder the terms: 6x2 = 8 + 7x Solving 6x2 = 8 + 7x Solving for variable 'x'. Reorder the terms: -8 + -7x + 6x2 = 8 + 7x + -8 + -7x Reorder the terms: -8 + -7x + 6x2 = 8 + -8 + 7x + -7x Combine like terms: 8 + -8 = 0 -8 + -7x + 6x2 = 0 + 7x + -7x -8 + -7x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -8 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.166666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.166666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 1.333333333 -1.166666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.166666667x + x2 = 1.333333333 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 = 1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 1.333333333 + 0.3402777780 Combine like terms: 1.333333333 + 0.3402777780 = 1.673611111 0.3402777780 + -1.166666667x + x2 = 1.673611111 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.673611111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.293681225 and -1.293681225.Subproblem 1
x + -0.5833333335 = 1.293681225 Simplifying x + -0.5833333335 = 1.293681225 Reorder the terms: -0.5833333335 + x = 1.293681225 Solving -0.5833333335 + x = 1.293681225 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 = 1.293681225 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.293681225 + 0.5833333335 x = 1.293681225 + 0.5833333335 Combine like terms: 1.293681225 + 0.5833333335 = 1.8770145585 x = 1.8770145585 Simplifying x = 1.8770145585Subproblem 2
x + -0.5833333335 = -1.293681225 Simplifying x + -0.5833333335 = -1.293681225 Reorder the terms: -0.5833333335 + x = -1.293681225 Solving -0.5833333335 + x = -1.293681225 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 = -1.293681225 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.293681225 + 0.5833333335 x = -1.293681225 + 0.5833333335 Combine like terms: -1.293681225 + 0.5833333335 = -0.7103478915 x = -0.7103478915 Simplifying x = -0.7103478915Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8770145585, -0.7103478915}
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