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Simplifying (2x + -1)(x + -5) + (2x + -1)(x + -2) = 0 Reorder the terms: (-1 + 2x)(x + -5) + (2x + -1)(x + -2) = 0 Reorder the terms: (-1 + 2x)(-5 + x) + (2x + -1)(x + -2) = 0 Multiply (-1 + 2x) * (-5 + x) (-1(-5 + x) + 2x * (-5 + x)) + (2x + -1)(x + -2) = 0 ((-5 * -1 + x * -1) + 2x * (-5 + x)) + (2x + -1)(x + -2) = 0 ((5 + -1x) + 2x * (-5 + x)) + (2x + -1)(x + -2) = 0 (5 + -1x + (-5 * 2x + x * 2x)) + (2x + -1)(x + -2) = 0 (5 + -1x + (-10x + 2x2)) + (2x + -1)(x + -2) = 0 Combine like terms: -1x + -10x = -11x (5 + -11x + 2x2) + (2x + -1)(x + -2) = 0 Reorder the terms: 5 + -11x + 2x2 + (-1 + 2x)(x + -2) = 0 Reorder the terms: 5 + -11x + 2x2 + (-1 + 2x)(-2 + x) = 0 Multiply (-1 + 2x) * (-2 + x) 5 + -11x + 2x2 + (-1(-2 + x) + 2x * (-2 + x)) = 0 5 + -11x + 2x2 + ((-2 * -1 + x * -1) + 2x * (-2 + x)) = 0 5 + -11x + 2x2 + ((2 + -1x) + 2x * (-2 + x)) = 0 5 + -11x + 2x2 + (2 + -1x + (-2 * 2x + x * 2x)) = 0 5 + -11x + 2x2 + (2 + -1x + (-4x + 2x2)) = 0 Combine like terms: -1x + -4x = -5x 5 + -11x + 2x2 + (2 + -5x + 2x2) = 0 Reorder the terms: 5 + 2 + -11x + -5x + 2x2 + 2x2 = 0 Combine like terms: 5 + 2 = 7 7 + -11x + -5x + 2x2 + 2x2 = 0 Combine like terms: -11x + -5x = -16x 7 + -16x + 2x2 + 2x2 = 0 Combine like terms: 2x2 + 2x2 = 4x2 7 + -16x + 4x2 = 0 Solving 7 + -16x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -2x)(7 + -2x) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {0.5, 3.5}
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