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Simplifying 6x2 = 7x + 6 Reorder the terms: 6x2 = 6 + 7x Solving 6x2 = 6 + 7x Solving for variable 'x'. Reorder the terms: -6 + -7x + 6x2 = 6 + 7x + -6 + -7x Reorder the terms: -6 + -7x + 6x2 = 6 + -6 + 7x + -7x Combine like terms: 6 + -6 = 0 -6 + -7x + 6x2 = 0 + 7x + -7x -6 + -7x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -6 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.166666667x + x2 = 0 + 1 -1.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.166666667x + x2 = 1 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 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + -1.166666667x + x2 = 1.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
x + -0.5833333335 = 1.157703666 Simplifying x + -0.5833333335 = 1.157703666 Reorder the terms: -0.5833333335 + x = 1.157703666 Solving -0.5833333335 + x = 1.157703666 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 = 1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.157703666 + 0.5833333335 x = 1.157703666 + 0.5833333335 Combine like terms: 1.157703666 + 0.5833333335 = 1.7410369995 x = 1.7410369995 Simplifying x = 1.7410369995Subproblem 2
x + -0.5833333335 = -1.157703666 Simplifying x + -0.5833333335 = -1.157703666 Reorder the terms: -0.5833333335 + x = -1.157703666 Solving -0.5833333335 + x = -1.157703666 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 = -1.157703666 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.157703666 + 0.5833333335 x = -1.157703666 + 0.5833333335 Combine like terms: -1.157703666 + 0.5833333335 = -0.5743703325 x = -0.5743703325 Simplifying x = -0.5743703325Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7410369995, -0.5743703325}
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