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Simplifying 6x2 + 7x + -120 = 0 Reorder the terms: -120 + 7x + 6x2 = 0 Solving -120 + 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'. -20 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.166666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.166666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.166666667x + x2 = 0 + 20 1.166666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.166666667x + x2 = 20 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 = 20 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 20 + 0.3402777780 Combine like terms: 20 + 0.3402777780 = 20.340277778 0.3402777780 + 1.166666667x + x2 = 20.340277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 20.340277778 Calculate the square root of the right side: 4.510019709 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 4.510019709 and -4.510019709.Subproblem 1
x + 0.5833333335 = 4.510019709 Simplifying x + 0.5833333335 = 4.510019709 Reorder the terms: 0.5833333335 + x = 4.510019709 Solving 0.5833333335 + x = 4.510019709 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 = 4.510019709 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 4.510019709 + -0.5833333335 x = 4.510019709 + -0.5833333335 Combine like terms: 4.510019709 + -0.5833333335 = 3.9266863755 x = 3.9266863755 Simplifying x = 3.9266863755Subproblem 2
x + 0.5833333335 = -4.510019709 Simplifying x + 0.5833333335 = -4.510019709 Reorder the terms: 0.5833333335 + x = -4.510019709 Solving 0.5833333335 + x = -4.510019709 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 = -4.510019709 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -4.510019709 + -0.5833333335 x = -4.510019709 + -0.5833333335 Combine like terms: -4.510019709 + -0.5833333335 = -5.0933530425 x = -5.0933530425 Simplifying x = -5.0933530425Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9266863755, -5.0933530425}
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