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Simplifying 6x2 + -7x + -13824 = 0 Reorder the terms: -13824 + -7x + 6x2 = 0 Solving -13824 + -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'. -2304 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '2304' to each side of the equation. -2304 + -1.166666667x + 2304 + x2 = 0 + 2304 Reorder the terms: -2304 + 2304 + -1.166666667x + x2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + -1.166666667x + x2 = 0 + 2304 -1.166666667x + x2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 -1.166666667x + x2 = 2304 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 = 2304 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 2304 + 0.3402777780 Combine like terms: 2304 + 0.3402777780 = 2304.340277778 0.3402777780 + -1.166666667x + x2 = 2304.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 2304.340277778 Calculate the square root of the right side: 48.003544429 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 48.003544429 and -48.003544429.Subproblem 1
x + -0.5833333335 = 48.003544429 Simplifying x + -0.5833333335 = 48.003544429 Reorder the terms: -0.5833333335 + x = 48.003544429 Solving -0.5833333335 + x = 48.003544429 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 = 48.003544429 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 48.003544429 + 0.5833333335 x = 48.003544429 + 0.5833333335 Combine like terms: 48.003544429 + 0.5833333335 = 48.5868777625 x = 48.5868777625 Simplifying x = 48.5868777625Subproblem 2
x + -0.5833333335 = -48.003544429 Simplifying x + -0.5833333335 = -48.003544429 Reorder the terms: -0.5833333335 + x = -48.003544429 Solving -0.5833333335 + x = -48.003544429 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 = -48.003544429 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -48.003544429 + 0.5833333335 x = -48.003544429 + 0.5833333335 Combine like terms: -48.003544429 + 0.5833333335 = -47.4202110955 x = -47.4202110955 Simplifying x = -47.4202110955Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.5868777625, -47.4202110955}
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