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Simplifying 3x(x + 2) + 2(x + -4) = 4x + 1 Reorder the terms: 3x(2 + x) + 2(x + -4) = 4x + 1 (2 * 3x + x * 3x) + 2(x + -4) = 4x + 1 (6x + 3x2) + 2(x + -4) = 4x + 1 Reorder the terms: 6x + 3x2 + 2(-4 + x) = 4x + 1 6x + 3x2 + (-4 * 2 + x * 2) = 4x + 1 6x + 3x2 + (-8 + 2x) = 4x + 1 Reorder the terms: -8 + 6x + 2x + 3x2 = 4x + 1 Combine like terms: 6x + 2x = 8x -8 + 8x + 3x2 = 4x + 1 Reorder the terms: -8 + 8x + 3x2 = 1 + 4x Solving -8 + 8x + 3x2 = 1 + 4x Solving for variable 'x'. Reorder the terms: -8 + -1 + 8x + -4x + 3x2 = 1 + 4x + -1 + -4x Combine like terms: -8 + -1 = -9 -9 + 8x + -4x + 3x2 = 1 + 4x + -1 + -4x Combine like terms: 8x + -4x = 4x -9 + 4x + 3x2 = 1 + 4x + -1 + -4x Reorder the terms: -9 + 4x + 3x2 = 1 + -1 + 4x + -4x Combine like terms: 1 + -1 = 0 -9 + 4x + 3x2 = 0 + 4x + -4x -9 + 4x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -9 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.333333333x + x2 = 0 + 3 1.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.333333333x + x2 = 3 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 3 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 3 + 0.4444444442 Combine like terms: 3 + 0.4444444442 = 3.4444444442 0.4444444442 + 1.333333333x + x2 = 3.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 3.4444444442 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.855921454 and -1.855921454.Subproblem 1
x + 0.6666666665 = 1.855921454 Simplifying x + 0.6666666665 = 1.855921454 Reorder the terms: 0.6666666665 + x = 1.855921454 Solving 0.6666666665 + x = 1.855921454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.855921454 + -0.6666666665 x = 1.855921454 + -0.6666666665 Combine like terms: 1.855921454 + -0.6666666665 = 1.1892547875 x = 1.1892547875 Simplifying x = 1.1892547875Subproblem 2
x + 0.6666666665 = -1.855921454 Simplifying x + 0.6666666665 = -1.855921454 Reorder the terms: 0.6666666665 + x = -1.855921454 Solving 0.6666666665 + x = -1.855921454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.855921454 + -0.6666666665 x = -1.855921454 + -0.6666666665 Combine like terms: -1.855921454 + -0.6666666665 = -2.5225881205 x = -2.5225881205 Simplifying x = -2.5225881205Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1892547875, -2.5225881205}
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