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Simplifying 3x + -2 = (2x + 1)(1 + -2x) Reorder the terms: -2 + 3x = (2x + 1)(1 + -2x) Reorder the terms: -2 + 3x = (1 + 2x)(1 + -2x) Multiply (1 + 2x) * (1 + -2x) -2 + 3x = (1(1 + -2x) + 2x * (1 + -2x)) -2 + 3x = ((1 * 1 + -2x * 1) + 2x * (1 + -2x)) -2 + 3x = ((1 + -2x) + 2x * (1 + -2x)) -2 + 3x = (1 + -2x + (1 * 2x + -2x * 2x)) -2 + 3x = (1 + -2x + (2x + -4x2)) Combine like terms: -2x + 2x = 0 -2 + 3x = (1 + 0 + -4x2) -2 + 3x = (1 + -4x2) Solving -2 + 3x = 1 + -4x2 Solving for variable 'x'. Reorder the terms: -2 + -1 + 3x + 4x2 = 1 + -4x2 + -1 + 4x2 Combine like terms: -2 + -1 = -3 -3 + 3x + 4x2 = 1 + -4x2 + -1 + 4x2 Reorder the terms: -3 + 3x + 4x2 = 1 + -1 + -4x2 + 4x2 Combine like terms: 1 + -1 = 0 -3 + 3x + 4x2 = 0 + -4x2 + 4x2 -3 + 3x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.75x + x2 = 0 + 0.75 0.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.75x + x2 = 0.75 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + 0.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 0.375 = 0.943729304 Simplifying x + 0.375 = 0.943729304 Reorder the terms: 0.375 + x = 0.943729304 Solving 0.375 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.943729304 + -0.375 x = 0.943729304 + -0.375 Combine like terms: 0.943729304 + -0.375 = 0.568729304 x = 0.568729304 Simplifying x = 0.568729304Subproblem 2
x + 0.375 = -0.943729304 Simplifying x + 0.375 = -0.943729304 Reorder the terms: 0.375 + x = -0.943729304 Solving 0.375 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.943729304 + -0.375 x = -0.943729304 + -0.375 Combine like terms: -0.943729304 + -0.375 = -1.318729304 x = -1.318729304 Simplifying x = -1.318729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.568729304, -1.318729304}
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