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Simplifying 6x2 + -7x = 31 Reorder the terms: -7x + 6x2 = 31 Solving -7x + 6x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + -7x + 6x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.166666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '5.166666667' to each side of the equation. -5.166666667 + -1.166666667x + 5.166666667 + x2 = 0 + 5.166666667 Reorder the terms: -5.166666667 + 5.166666667 + -1.166666667x + x2 = 0 + 5.166666667 Combine like terms: -5.166666667 + 5.166666667 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 5.166666667 -1.166666667x + x2 = 0 + 5.166666667 Combine like terms: 0 + 5.166666667 = 5.166666667 -1.166666667x + x2 = 5.166666667 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 = 5.166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 5.166666667 + 0.3402777780 Combine like terms: 5.166666667 + 0.3402777780 = 5.506944445 0.3402777780 + -1.166666667x + x2 = 5.506944445 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 5.506944445 Calculate the square root of the right side: 2.346687974 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 2.346687974 and -2.346687974.Subproblem 1
x + -0.5833333335 = 2.346687974 Simplifying x + -0.5833333335 = 2.346687974 Reorder the terms: -0.5833333335 + x = 2.346687974 Solving -0.5833333335 + x = 2.346687974 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 = 2.346687974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.346687974 + 0.5833333335 x = 2.346687974 + 0.5833333335 Combine like terms: 2.346687974 + 0.5833333335 = 2.9300213075 x = 2.9300213075 Simplifying x = 2.9300213075Subproblem 2
x + -0.5833333335 = -2.346687974 Simplifying x + -0.5833333335 = -2.346687974 Reorder the terms: -0.5833333335 + x = -2.346687974 Solving -0.5833333335 + x = -2.346687974 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 = -2.346687974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.346687974 + 0.5833333335 x = -2.346687974 + 0.5833333335 Combine like terms: -2.346687974 + 0.5833333335 = -1.7633546405 x = -1.7633546405 Simplifying x = -1.7633546405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9300213075, -1.7633546405}
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