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Simplifying 6x(4 + -3x) + -5x(x + -4) + -1(9x + 2) = 0 (4 * 6x + -3x * 6x) + -5x(x + -4) + -1(9x + 2) = 0 (24x + -18x2) + -5x(x + -4) + -1(9x + 2) = 0 Reorder the terms: 24x + -18x2 + -5x(-4 + x) + -1(9x + 2) = 0 24x + -18x2 + (-4 * -5x + x * -5x) + -1(9x + 2) = 0 24x + -18x2 + (20x + -5x2) + -1(9x + 2) = 0 Reorder the terms: 24x + -18x2 + 20x + -5x2 + -1(2 + 9x) = 0 24x + -18x2 + 20x + -5x2 + (2 * -1 + 9x * -1) = 0 24x + -18x2 + 20x + -5x2 + (-2 + -9x) = 0 Reorder the terms: -2 + 24x + 20x + -9x + -18x2 + -5x2 = 0 Combine like terms: 24x + 20x = 44x -2 + 44x + -9x + -18x2 + -5x2 = 0 Combine like terms: 44x + -9x = 35x -2 + 35x + -18x2 + -5x2 = 0 Combine like terms: -18x2 + -5x2 = -23x2 -2 + 35x + -23x2 = 0 Solving -2 + 35x + -23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -23 the coefficient of the squared term: Divide each side by '-23'. 0.08695652174 + -1.52173913x + x2 = 0 Move the constant term to the right: Add '-0.08695652174' to each side of the equation. 0.08695652174 + -1.52173913x + -0.08695652174 + x2 = 0 + -0.08695652174 Reorder the terms: 0.08695652174 + -0.08695652174 + -1.52173913x + x2 = 0 + -0.08695652174 Combine like terms: 0.08695652174 + -0.08695652174 = 0.00000000000 0.00000000000 + -1.52173913x + x2 = 0 + -0.08695652174 -1.52173913x + x2 = 0 + -0.08695652174 Combine like terms: 0 + -0.08695652174 = -0.08695652174 -1.52173913x + x2 = -0.08695652174 The x term is -1.52173913x. Take half its coefficient (-0.760869565). Square it (0.5789224949) and add it to both sides. Add '0.5789224949' to each side of the equation. -1.52173913x + 0.5789224949 + x2 = -0.08695652174 + 0.5789224949 Reorder the terms: 0.5789224949 + -1.52173913x + x2 = -0.08695652174 + 0.5789224949 Combine like terms: -0.08695652174 + 0.5789224949 = 0.49196597316 0.5789224949 + -1.52173913x + x2 = 0.49196597316 Factor a perfect square on the left side: (x + -0.760869565)(x + -0.760869565) = 0.49196597316 Calculate the square root of the right side: 0.701402861 Break this problem into two subproblems by setting (x + -0.760869565) equal to 0.701402861 and -0.701402861.Subproblem 1
x + -0.760869565 = 0.701402861 Simplifying x + -0.760869565 = 0.701402861 Reorder the terms: -0.760869565 + x = 0.701402861 Solving -0.760869565 + x = 0.701402861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.760869565' to each side of the equation. -0.760869565 + 0.760869565 + x = 0.701402861 + 0.760869565 Combine like terms: -0.760869565 + 0.760869565 = 0.000000000 0.000000000 + x = 0.701402861 + 0.760869565 x = 0.701402861 + 0.760869565 Combine like terms: 0.701402861 + 0.760869565 = 1.462272426 x = 1.462272426 Simplifying x = 1.462272426Subproblem 2
x + -0.760869565 = -0.701402861 Simplifying x + -0.760869565 = -0.701402861 Reorder the terms: -0.760869565 + x = -0.701402861 Solving -0.760869565 + x = -0.701402861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.760869565' to each side of the equation. -0.760869565 + 0.760869565 + x = -0.701402861 + 0.760869565 Combine like terms: -0.760869565 + 0.760869565 = 0.000000000 0.000000000 + x = -0.701402861 + 0.760869565 x = -0.701402861 + 0.760869565 Combine like terms: -0.701402861 + 0.760869565 = 0.059466704 x = 0.059466704 Simplifying x = 0.059466704Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.462272426, 0.059466704}
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