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Simplifying 6x2 + 7x + -313 = 0 Reorder the terms: -313 + 7x + 6x2 = 0 Solving -313 + 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'. -52.16666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '52.16666667' to each side of the equation. -52.16666667 + 1.166666667x + 52.16666667 + x2 = 0 + 52.16666667 Reorder the terms: -52.16666667 + 52.16666667 + 1.166666667x + x2 = 0 + 52.16666667 Combine like terms: -52.16666667 + 52.16666667 = 0.00000000 0.00000000 + 1.166666667x + x2 = 0 + 52.16666667 1.166666667x + x2 = 0 + 52.16666667 Combine like terms: 0 + 52.16666667 = 52.16666667 1.166666667x + x2 = 52.16666667 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 = 52.16666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 52.16666667 + 0.3402777780 Combine like terms: 52.16666667 + 0.3402777780 = 52.506944448 0.3402777780 + 1.166666667x + x2 = 52.506944448 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 52.506944448 Calculate the square root of the right side: 7.24616757 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 7.24616757 and -7.24616757.Subproblem 1
x + 0.5833333335 = 7.24616757 Simplifying x + 0.5833333335 = 7.24616757 Reorder the terms: 0.5833333335 + x = 7.24616757 Solving 0.5833333335 + x = 7.24616757 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 = 7.24616757 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 7.24616757 + -0.5833333335 x = 7.24616757 + -0.5833333335 Combine like terms: 7.24616757 + -0.5833333335 = 6.6628342365 x = 6.6628342365 Simplifying x = 6.6628342365Subproblem 2
x + 0.5833333335 = -7.24616757 Simplifying x + 0.5833333335 = -7.24616757 Reorder the terms: 0.5833333335 + x = -7.24616757 Solving 0.5833333335 + x = -7.24616757 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 = -7.24616757 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -7.24616757 + -0.5833333335 x = -7.24616757 + -0.5833333335 Combine like terms: -7.24616757 + -0.5833333335 = -7.8295009035 x = -7.8295009035 Simplifying x = -7.8295009035Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6628342365, -7.8295009035}
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