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Simplifying 6x2 + 7x + -36 = 0 Reorder the terms: -36 + 7x + 6x2 = 0 Solving -36 + 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'. -6 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.166666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.166666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.166666667x + x2 = 0 + 6 1.166666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.166666667x + x2 = 6 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 = 6 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 6 + 0.3402777780 Combine like terms: 6 + 0.3402777780 = 6.340277778 0.3402777780 + 1.166666667x + x2 = 6.340277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 6.340277778 Calculate the square root of the right side: 2.517990822 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 2.517990822 and -2.517990822.Subproblem 1
x + 0.5833333335 = 2.517990822 Simplifying x + 0.5833333335 = 2.517990822 Reorder the terms: 0.5833333335 + x = 2.517990822 Solving 0.5833333335 + x = 2.517990822 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 = 2.517990822 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 2.517990822 + -0.5833333335 x = 2.517990822 + -0.5833333335 Combine like terms: 2.517990822 + -0.5833333335 = 1.9346574885 x = 1.9346574885 Simplifying x = 1.9346574885Subproblem 2
x + 0.5833333335 = -2.517990822 Simplifying x + 0.5833333335 = -2.517990822 Reorder the terms: 0.5833333335 + x = -2.517990822 Solving 0.5833333335 + x = -2.517990822 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 = -2.517990822 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -2.517990822 + -0.5833333335 x = -2.517990822 + -0.5833333335 Combine like terms: -2.517990822 + -0.5833333335 = -3.1013241555 x = -3.1013241555 Simplifying x = -3.1013241555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9346574885, -3.1013241555}
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