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Simplifying (2x + -5)(x + -4) + 2x(1 + -1x) = 0 Reorder the terms: (-5 + 2x)(x + -4) + 2x(1 + -1x) = 0 Reorder the terms: (-5 + 2x)(-4 + x) + 2x(1 + -1x) = 0 Multiply (-5 + 2x) * (-4 + x) (-5(-4 + x) + 2x * (-4 + x)) + 2x(1 + -1x) = 0 ((-4 * -5 + x * -5) + 2x * (-4 + x)) + 2x(1 + -1x) = 0 ((20 + -5x) + 2x * (-4 + x)) + 2x(1 + -1x) = 0 (20 + -5x + (-4 * 2x + x * 2x)) + 2x(1 + -1x) = 0 (20 + -5x + (-8x + 2x2)) + 2x(1 + -1x) = 0 Combine like terms: -5x + -8x = -13x (20 + -13x + 2x2) + 2x(1 + -1x) = 0 20 + -13x + 2x2 + (1 * 2x + -1x * 2x) = 0 20 + -13x + 2x2 + (2x + -2x2) = 0 Reorder the terms: 20 + -13x + 2x + 2x2 + -2x2 = 0 Combine like terms: -13x + 2x = -11x 20 + -11x + 2x2 + -2x2 = 0 Combine like terms: 2x2 + -2x2 = 0 20 + -11x + 0 = 0 20 + -11x = 0 Solving 20 + -11x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -11x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -11x = 0 + -20 -11x = 0 + -20 Combine like terms: 0 + -20 = -20 -11x = -20 Divide each side by '-11'. x = 1.818181818 Simplifying x = 1.818181818
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