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Simplifying (8x + -1)(2x + 1) = 3x Reorder the terms: (-1 + 8x)(2x + 1) = 3x Reorder the terms: (-1 + 8x)(1 + 2x) = 3x Multiply (-1 + 8x) * (1 + 2x) (-1(1 + 2x) + 8x * (1 + 2x)) = 3x ((1 * -1 + 2x * -1) + 8x * (1 + 2x)) = 3x ((-1 + -2x) + 8x * (1 + 2x)) = 3x (-1 + -2x + (1 * 8x + 2x * 8x)) = 3x (-1 + -2x + (8x + 16x2)) = 3x Combine like terms: -2x + 8x = 6x (-1 + 6x + 16x2) = 3x Solving -1 + 6x + 16x2 = 3x Solving for variable 'x'. Reorder the terms: -1 + 6x + -3x + 16x2 = 3x + -3x Combine like terms: 6x + -3x = 3x -1 + 3x + 16x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -1 + 3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 0.1875x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.1875x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.1875x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.1875x + x2 = 0 + 0.0625 0.1875x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.1875x + x2 = 0.0625 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 0.0625 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 0.0625 + 0.0087890625 Combine like terms: 0.0625 + 0.0087890625 = 0.0712890625 0.0087890625 + 0.1875x + x2 = 0.0712890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 0.0712890625 Calculate the square root of the right side: 0.267000117 Break this problem into two subproblems by setting (x + 0.09375) equal to 0.267000117 and -0.267000117.Subproblem 1
x + 0.09375 = 0.267000117 Simplifying x + 0.09375 = 0.267000117 Reorder the terms: 0.09375 + x = 0.267000117 Solving 0.09375 + x = 0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 0.267000117 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 0.267000117 + -0.09375 x = 0.267000117 + -0.09375 Combine like terms: 0.267000117 + -0.09375 = 0.173250117 x = 0.173250117 Simplifying x = 0.173250117Subproblem 2
x + 0.09375 = -0.267000117 Simplifying x + 0.09375 = -0.267000117 Reorder the terms: 0.09375 + x = -0.267000117 Solving 0.09375 + x = -0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -0.267000117 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -0.267000117 + -0.09375 x = -0.267000117 + -0.09375 Combine like terms: -0.267000117 + -0.09375 = -0.360750117 x = -0.360750117 Simplifying x = -0.360750117Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.173250117, -0.360750117}
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