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Simplifying 6x(4 + 7x) = x + x + -1x + 4x + 2 (4 * 6x + 7x * 6x) = x + x + -1x + 4x + 2 (24x + 42x2) = x + x + -1x + 4x + 2 Reorder the terms: 24x + 42x2 = 2 + x + x + -1x + 4x Combine like terms: x + x = 2x 24x + 42x2 = 2 + 2x + -1x + 4x Combine like terms: 2x + -1x = 1x 24x + 42x2 = 2 + 1x + 4x Combine like terms: 1x + 4x = 5x 24x + 42x2 = 2 + 5x Solving 24x + 42x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -2 + 24x + -5x + 42x2 = 2 + 5x + -2 + -5x Combine like terms: 24x + -5x = 19x -2 + 19x + 42x2 = 2 + 5x + -2 + -5x Reorder the terms: -2 + 19x + 42x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -2 + 19x + 42x2 = 0 + 5x + -5x -2 + 19x + 42x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + 19x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.04761904762 + 0.4523809524x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.4523809524x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + 0.4523809524x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + 0.4523809524x + x2 = 0 + 0.04761904762 0.4523809524x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 0.4523809524x + x2 = 0.04761904762 The x term is 0.4523809524x. Take half its coefficient (0.2261904762). Square it (0.05116213152) and add it to both sides. Add '0.05116213152' to each side of the equation. 0.4523809524x + 0.05116213152 + x2 = 0.04761904762 + 0.05116213152 Reorder the terms: 0.05116213152 + 0.4523809524x + x2 = 0.04761904762 + 0.05116213152 Combine like terms: 0.04761904762 + 0.05116213152 = 0.09878117914 0.05116213152 + 0.4523809524x + x2 = 0.09878117914 Factor a perfect square on the left side: (x + 0.2261904762)(x + 0.2261904762) = 0.09878117914 Calculate the square root of the right side: 0.314294733 Break this problem into two subproblems by setting (x + 0.2261904762) equal to 0.314294733 and -0.314294733.Subproblem 1
x + 0.2261904762 = 0.314294733 Simplifying x + 0.2261904762 = 0.314294733 Reorder the terms: 0.2261904762 + x = 0.314294733 Solving 0.2261904762 + x = 0.314294733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2261904762' to each side of the equation. 0.2261904762 + -0.2261904762 + x = 0.314294733 + -0.2261904762 Combine like terms: 0.2261904762 + -0.2261904762 = 0.0000000000 0.0000000000 + x = 0.314294733 + -0.2261904762 x = 0.314294733 + -0.2261904762 Combine like terms: 0.314294733 + -0.2261904762 = 0.0881042568 x = 0.0881042568 Simplifying x = 0.0881042568Subproblem 2
x + 0.2261904762 = -0.314294733 Simplifying x + 0.2261904762 = -0.314294733 Reorder the terms: 0.2261904762 + x = -0.314294733 Solving 0.2261904762 + x = -0.314294733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2261904762' to each side of the equation. 0.2261904762 + -0.2261904762 + x = -0.314294733 + -0.2261904762 Combine like terms: 0.2261904762 + -0.2261904762 = 0.0000000000 0.0000000000 + x = -0.314294733 + -0.2261904762 x = -0.314294733 + -0.2261904762 Combine like terms: -0.314294733 + -0.2261904762 = -0.5404852092 x = -0.5404852092 Simplifying x = -0.5404852092Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0881042568, -0.5404852092}
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