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Simplifying 6x2 + -7x = 140 Reorder the terms: -7x + 6x2 = 140 Solving -7x + 6x2 = 140 Solving for variable 'x'. Reorder the terms: -140 + -7x + 6x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -23.33333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -1.166666667x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -1.166666667x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 23.33333333 -1.166666667x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -1.166666667x + x2 = 23.33333333 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 = 23.33333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 23.33333333 + 0.3402777780 Combine like terms: 23.33333333 + 0.3402777780 = 23.673611108 0.3402777780 + -1.166666667x + x2 = 23.673611108 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 23.673611108 Calculate the square root of the right side: 4.865553525 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 4.865553525 and -4.865553525.Subproblem 1
x + -0.5833333335 = 4.865553525 Simplifying x + -0.5833333335 = 4.865553525 Reorder the terms: -0.5833333335 + x = 4.865553525 Solving -0.5833333335 + x = 4.865553525 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 = 4.865553525 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 4.865553525 + 0.5833333335 x = 4.865553525 + 0.5833333335 Combine like terms: 4.865553525 + 0.5833333335 = 5.4488868585 x = 5.4488868585 Simplifying x = 5.4488868585Subproblem 2
x + -0.5833333335 = -4.865553525 Simplifying x + -0.5833333335 = -4.865553525 Reorder the terms: -0.5833333335 + x = -4.865553525 Solving -0.5833333335 + x = -4.865553525 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 = -4.865553525 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -4.865553525 + 0.5833333335 x = -4.865553525 + 0.5833333335 Combine like terms: -4.865553525 + 0.5833333335 = -4.2822201915 x = -4.2822201915 Simplifying x = -4.2822201915Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4488868585, -4.2822201915}
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