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Simplifying 6x2 + 7x + -64 = 0 Reorder the terms: -64 + 7x + 6x2 = 0 Solving -64 + 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'. -10.66666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 1.166666667x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 1.166666667x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 1.166666667x + x2 = 0 + 10.66666667 1.166666667x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 1.166666667x + x2 = 10.66666667 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 = 10.66666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 10.66666667 + 0.3402777780 Combine like terms: 10.66666667 + 0.3402777780 = 11.006944448 0.3402777780 + 1.166666667x + x2 = 11.006944448 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 11.006944448 Calculate the square root of the right side: 3.31767154 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 3.31767154 and -3.31767154.Subproblem 1
x + 0.5833333335 = 3.31767154 Simplifying x + 0.5833333335 = 3.31767154 Reorder the terms: 0.5833333335 + x = 3.31767154 Solving 0.5833333335 + x = 3.31767154 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 = 3.31767154 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 3.31767154 + -0.5833333335 x = 3.31767154 + -0.5833333335 Combine like terms: 3.31767154 + -0.5833333335 = 2.7343382065 x = 2.7343382065 Simplifying x = 2.7343382065Subproblem 2
x + 0.5833333335 = -3.31767154 Simplifying x + 0.5833333335 = -3.31767154 Reorder the terms: 0.5833333335 + x = -3.31767154 Solving 0.5833333335 + x = -3.31767154 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 = -3.31767154 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -3.31767154 + -0.5833333335 x = -3.31767154 + -0.5833333335 Combine like terms: -3.31767154 + -0.5833333335 = -3.9010048735 x = -3.9010048735 Simplifying x = -3.9010048735Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7343382065, -3.9010048735}
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