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Simplifying 6x2 + 7x + -86 = 0 Reorder the terms: -86 + 7x + 6x2 = 0 Solving -86 + 7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -14.33333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '14.33333333' to each side of the equation. -14.33333333 + 1.166666667x + 14.33333333 + x2 = 0 + 14.33333333 Reorder the terms: -14.33333333 + 14.33333333 + 1.166666667x + x2 = 0 + 14.33333333 Combine like terms: -14.33333333 + 14.33333333 = 0.00000000 0.00000000 + 1.166666667x + x2 = 0 + 14.33333333 1.166666667x + x2 = 0 + 14.33333333 Combine like terms: 0 + 14.33333333 = 14.33333333 1.166666667x + x2 = 14.33333333 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 = 14.33333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 14.33333333 + 0.3402777780 Combine like terms: 14.33333333 + 0.3402777780 = 14.673611108 0.3402777780 + 1.166666667x + x2 = 14.673611108 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 14.673611108 Calculate the square root of the right side: 3.830614978 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 3.830614978 and -3.830614978.Subproblem 1
x + 0.5833333335 = 3.830614978 Simplifying x + 0.5833333335 = 3.830614978 Reorder the terms: 0.5833333335 + x = 3.830614978 Solving 0.5833333335 + x = 3.830614978 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 = 3.830614978 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 3.830614978 + -0.5833333335 x = 3.830614978 + -0.5833333335 Combine like terms: 3.830614978 + -0.5833333335 = 3.2472816445 x = 3.2472816445 Simplifying x = 3.2472816445Subproblem 2
x + 0.5833333335 = -3.830614978 Simplifying x + 0.5833333335 = -3.830614978 Reorder the terms: 0.5833333335 + x = -3.830614978 Solving 0.5833333335 + x = -3.830614978 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 = -3.830614978 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -3.830614978 + -0.5833333335 x = -3.830614978 + -0.5833333335 Combine like terms: -3.830614978 + -0.5833333335 = -4.4139483115 x = -4.4139483115 Simplifying x = -4.4139483115Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2472816445, -4.4139483115}
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