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Simplifying (4x + -1)(2x + 3) = 3x Reorder the terms: (-1 + 4x)(2x + 3) = 3x Reorder the terms: (-1 + 4x)(3 + 2x) = 3x Multiply (-1 + 4x) * (3 + 2x) (-1(3 + 2x) + 4x * (3 + 2x)) = 3x ((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = 3x ((-3 + -2x) + 4x * (3 + 2x)) = 3x (-3 + -2x + (3 * 4x + 2x * 4x)) = 3x (-3 + -2x + (12x + 8x2)) = 3x Combine like terms: -2x + 12x = 10x (-3 + 10x + 8x2) = 3x Solving -3 + 10x + 8x2 = 3x Solving for variable 'x'. Reorder the terms: -3 + 10x + -3x + 8x2 = 3x + -3x Combine like terms: 10x + -3x = 7x -3 + 7x + 8x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -3 + 7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 0.875x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.875x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.875x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.875x + x2 = 0 + 0.375 0.875x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.875x + x2 = 0.375 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + 0.875x + x2 = 0.56640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
x + 0.4375 = 0.752599661 Simplifying x + 0.4375 = 0.752599661 Reorder the terms: 0.4375 + x = 0.752599661 Solving 0.4375 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.752599661 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.752599661 + -0.4375 x = 0.752599661 + -0.4375 Combine like terms: 0.752599661 + -0.4375 = 0.315099661 x = 0.315099661 Simplifying x = 0.315099661Subproblem 2
x + 0.4375 = -0.752599661 Simplifying x + 0.4375 = -0.752599661 Reorder the terms: 0.4375 + x = -0.752599661 Solving 0.4375 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.752599661 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.752599661 + -0.4375 x = -0.752599661 + -0.4375 Combine like terms: -0.752599661 + -0.4375 = -1.190099661 x = -1.190099661 Simplifying x = -1.190099661Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.315099661, -1.190099661}
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