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Simplifying (2x + -1)(x + 7) + (6x + -2)(2x + -1) = 0 Reorder the terms: (-1 + 2x)(x + 7) + (6x + -2)(2x + -1) = 0 Reorder the terms: (-1 + 2x)(7 + x) + (6x + -2)(2x + -1) = 0 Multiply (-1 + 2x) * (7 + x) (-1(7 + x) + 2x * (7 + x)) + (6x + -2)(2x + -1) = 0 ((7 * -1 + x * -1) + 2x * (7 + x)) + (6x + -2)(2x + -1) = 0 ((-7 + -1x) + 2x * (7 + x)) + (6x + -2)(2x + -1) = 0 (-7 + -1x + (7 * 2x + x * 2x)) + (6x + -2)(2x + -1) = 0 (-7 + -1x + (14x + 2x2)) + (6x + -2)(2x + -1) = 0 Combine like terms: -1x + 14x = 13x (-7 + 13x + 2x2) + (6x + -2)(2x + -1) = 0 Reorder the terms: -7 + 13x + 2x2 + (-2 + 6x)(2x + -1) = 0 Reorder the terms: -7 + 13x + 2x2 + (-2 + 6x)(-1 + 2x) = 0 Multiply (-2 + 6x) * (-1 + 2x) -7 + 13x + 2x2 + (-2(-1 + 2x) + 6x * (-1 + 2x)) = 0 -7 + 13x + 2x2 + ((-1 * -2 + 2x * -2) + 6x * (-1 + 2x)) = 0 -7 + 13x + 2x2 + ((2 + -4x) + 6x * (-1 + 2x)) = 0 -7 + 13x + 2x2 + (2 + -4x + (-1 * 6x + 2x * 6x)) = 0 -7 + 13x + 2x2 + (2 + -4x + (-6x + 12x2)) = 0 Combine like terms: -4x + -6x = -10x -7 + 13x + 2x2 + (2 + -10x + 12x2) = 0 Reorder the terms: -7 + 2 + 13x + -10x + 2x2 + 12x2 = 0 Combine like terms: -7 + 2 = -5 -5 + 13x + -10x + 2x2 + 12x2 = 0 Combine like terms: 13x + -10x = 3x -5 + 3x + 2x2 + 12x2 = 0 Combine like terms: 2x2 + 12x2 = 14x2 -5 + 3x + 14x2 = 0 Solving -5 + 3x + 14x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -7x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + -7x)' equal to zero and attempt to solve: Simplifying -5 + -7x = 0 Solving -5 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7x = 0 + 5 -7x = 0 + 5 Combine like terms: 0 + 5 = 5 -7x = 5 Divide each side by '-7'. x = -0.7142857143 Simplifying x = -0.7142857143Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.7142857143, 0.5}
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