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Simplifying 2x + -1(3x + 5)(4x + -1) + 2 = 5x + (12 + 5)(-1x + 2) + -46 Reorder the terms: 2x + -1(5 + 3x)(4x + -1) + 2 = 5x + (12 + 5)(-1x + 2) + -46 Reorder the terms: 2x + -1(5 + 3x)(-1 + 4x) + 2 = 5x + (12 + 5)(-1x + 2) + -46 Multiply (5 + 3x) * (-1 + 4x) 2x + -1(5(-1 + 4x) + 3x * (-1 + 4x)) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + -1((-1 * 5 + 4x * 5) + 3x * (-1 + 4x)) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + -1((-5 + 20x) + 3x * (-1 + 4x)) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + -1(-5 + 20x + (-1 * 3x + 4x * 3x)) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + -1(-5 + 20x + (-3x + 12x2)) + 2 = 5x + (12 + 5)(-1x + 2) + -46 Combine like terms: 20x + -3x = 17x 2x + -1(-5 + 17x + 12x2) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + (-5 * -1 + 17x * -1 + 12x2 * -1) + 2 = 5x + (12 + 5)(-1x + 2) + -46 2x + (5 + -17x + -12x2) + 2 = 5x + (12 + 5)(-1x + 2) + -46 Reorder the terms: 5 + 2 + 2x + -17x + -12x2 = 5x + (12 + 5)(-1x + 2) + -46 Combine like terms: 5 + 2 = 7 7 + 2x + -17x + -12x2 = 5x + (12 + 5)(-1x + 2) + -46 Combine like terms: 2x + -17x = -15x 7 + -15x + -12x2 = 5x + (12 + 5)(-1x + 2) + -46 Combine like terms: 12 + 5 = 17 7 + -15x + -12x2 = 5x + (17)(-1x + 2) + -46 Reorder the terms: 7 + -15x + -12x2 = 5x + 17(2 + -1x) + -46 7 + -15x + -12x2 = 5x + (2 * 17 + -1x * 17) + -46 7 + -15x + -12x2 = 5x + (34 + -17x) + -46 Reorder the terms: 7 + -15x + -12x2 = 34 + -46 + 5x + -17x Combine like terms: 34 + -46 = -12 7 + -15x + -12x2 = -12 + 5x + -17x Combine like terms: 5x + -17x = -12x 7 + -15x + -12x2 = -12 + -12x Solving 7 + -15x + -12x2 = -12 + -12x Solving for variable 'x'. Reorder the terms: 7 + 12 + -15x + 12x + -12x2 = -12 + -12x + 12 + 12x Combine like terms: 7 + 12 = 19 19 + -15x + 12x + -12x2 = -12 + -12x + 12 + 12x Combine like terms: -15x + 12x = -3x 19 + -3x + -12x2 = -12 + -12x + 12 + 12x Reorder the terms: 19 + -3x + -12x2 = -12 + 12 + -12x + 12x Combine like terms: -12 + 12 = 0 19 + -3x + -12x2 = 0 + -12x + 12x 19 + -3x + -12x2 = -12x + 12x Combine like terms: -12x + 12x = 0 19 + -3x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.583333333 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + 0.25x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + 0.25x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 1.583333333 0.25x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 0.25x + x2 = 1.583333333 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.583333333 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.583333333 + 0.015625 Combine like terms: 1.583333333 + 0.015625 = 1.598958333 0.015625 + 0.25x + x2 = 1.598958333 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.598958333 Calculate the square root of the right side: 1.264499242 Break this problem into two subproblems by setting (x + 0.125) equal to 1.264499242 and -1.264499242.Subproblem 1
x + 0.125 = 1.264499242 Simplifying x + 0.125 = 1.264499242 Reorder the terms: 0.125 + x = 1.264499242 Solving 0.125 + x = 1.264499242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.264499242 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.264499242 + -0.125 x = 1.264499242 + -0.125 Combine like terms: 1.264499242 + -0.125 = 1.139499242 x = 1.139499242 Simplifying x = 1.139499242Subproblem 2
x + 0.125 = -1.264499242 Simplifying x + 0.125 = -1.264499242 Reorder the terms: 0.125 + x = -1.264499242 Solving 0.125 + x = -1.264499242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.264499242 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.264499242 + -0.125 x = -1.264499242 + -0.125 Combine like terms: -1.264499242 + -0.125 = -1.389499242 x = -1.389499242 Simplifying x = -1.389499242Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.139499242, -1.389499242}
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