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Simplifying (2x + -3) * 2 + (x + 1)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms: (-3 + 2x) * 2 + (x + 1)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms for easier multiplication: 2(-3 + 2x) + (x + 1)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 (-3 * 2 + 2x * 2) + (x + 1)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 (-6 + 4x) + (x + 1)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms: -6 + 4x + (1 + x)(x + -1) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms: -6 + 4x + (1 + x)(-1 + x) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Multiply (1 + x) * (-1 + x) -6 + 4x + (1(-1 + x) + x(-1 + x)) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 -6 + 4x + ((-1 * 1 + x * 1) + x(-1 + x)) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 -6 + 4x + ((-1 + 1x) + x(-1 + x)) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 -6 + 4x + (-1 + 1x + (-1 * x + x * x)) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 -6 + 4x + (-1 + 1x + (-1x + x2)) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Combine like terms: 1x + -1x = 0 -6 + 4x + (-1 + 0 + x2) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 -6 + 4x + (-1 + x2) + x = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms: -6 + -1 + 4x + x + x2 = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Combine like terms: -6 + -1 = -7 -7 + 4x + x + x2 = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Combine like terms: 4x + x = 5x -7 + 5x + x2 = (3x + -1) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms: -7 + 5x + x2 = (-1 + 3x) * 2 + (1 + -2x)(2x + 1) + -4 Reorder the terms for easier multiplication: -7 + 5x + x2 = 2(-1 + 3x) + (1 + -2x)(2x + 1) + -4 -7 + 5x + x2 = (-1 * 2 + 3x * 2) + (1 + -2x)(2x + 1) + -4 -7 + 5x + x2 = (-2 + 6x) + (1 + -2x)(2x + 1) + -4 Reorder the terms: -7 + 5x + x2 = -2 + 6x + (1 + -2x)(1 + 2x) + -4 Multiply (1 + -2x) * (1 + 2x) -7 + 5x + x2 = -2 + 6x + (1(1 + 2x) + -2x * (1 + 2x)) + -4 -7 + 5x + x2 = -2 + 6x + ((1 * 1 + 2x * 1) + -2x * (1 + 2x)) + -4 -7 + 5x + x2 = -2 + 6x + ((1 + 2x) + -2x * (1 + 2x)) + -4 -7 + 5x + x2 = -2 + 6x + (1 + 2x + (1 * -2x + 2x * -2x)) + -4 -7 + 5x + x2 = -2 + 6x + (1 + 2x + (-2x + -4x2)) + -4 Combine like terms: 2x + -2x = 0 -7 + 5x + x2 = -2 + 6x + (1 + 0 + -4x2) + -4 -7 + 5x + x2 = -2 + 6x + (1 + -4x2) + -4 Reorder the terms: -7 + 5x + x2 = -2 + 1 + -4 + 6x + -4x2 Combine like terms: -2 + 1 = -1 -7 + 5x + x2 = -1 + -4 + 6x + -4x2 Combine like terms: -1 + -4 = -5 -7 + 5x + x2 = -5 + 6x + -4x2 Solving -7 + 5x + x2 = -5 + 6x + -4x2 Solving for variable 'x'. Reorder the terms: -7 + 5 + 5x + -6x + x2 + 4x2 = -5 + 6x + -4x2 + 5 + -6x + 4x2 Combine like terms: -7 + 5 = -2 -2 + 5x + -6x + x2 + 4x2 = -5 + 6x + -4x2 + 5 + -6x + 4x2 Combine like terms: 5x + -6x = -1x -2 + -1x + x2 + 4x2 = -5 + 6x + -4x2 + 5 + -6x + 4x2 Combine like terms: x2 + 4x2 = 5x2 -2 + -1x + 5x2 = -5 + 6x + -4x2 + 5 + -6x + 4x2 Reorder the terms: -2 + -1x + 5x2 = -5 + 5 + 6x + -6x + -4x2 + 4x2 Combine like terms: -5 + 5 = 0 -2 + -1x + 5x2 = 0 + 6x + -6x + -4x2 + 4x2 -2 + -1x + 5x2 = 6x + -6x + -4x2 + 4x2 Combine like terms: 6x + -6x = 0 -2 + -1x + 5x2 = 0 + -4x2 + 4x2 -2 + -1x + 5x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.2x + x2 = 0 + 0.4 -0.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.2x + x2 = 0.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.4 + 0.01 Combine like terms: 0.4 + 0.01 = 0.41 0.01 + -0.2x + x2 = 0.41 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + -0.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + -0.1 = 0.640312424 Simplifying x + -0.1 = 0.640312424 Reorder the terms: -0.1 + x = 0.640312424 Solving -0.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.640312424 + 0.1 x = 0.640312424 + 0.1 Combine like terms: 0.640312424 + 0.1 = 0.740312424 x = 0.740312424 Simplifying x = 0.740312424Subproblem 2
x + -0.1 = -0.640312424 Simplifying x + -0.1 = -0.640312424 Reorder the terms: -0.1 + x = -0.640312424 Solving -0.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.640312424 + 0.1 x = -0.640312424 + 0.1 Combine like terms: -0.640312424 + 0.1 = -0.540312424 x = -0.540312424 Simplifying x = -0.540312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.740312424, -0.540312424}
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