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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 = 9x (-5 + 9x + 2x2) + (2x + -1)(x + -2) = 0 Reorder the terms: -5 + 9x + 2x2 + (-1 + 2x)(x + -2) = 0 Reorder the terms: -5 + 9x + 2x2 + (-1 + 2x)(-2 + x) = 0 Multiply (-1 + 2x) * (-2 + x) -5 + 9x + 2x2 + (-1(-2 + x) + 2x * (-2 + x)) = 0 -5 + 9x + 2x2 + ((-2 * -1 + x * -1) + 2x * (-2 + x)) = 0 -5 + 9x + 2x2 + ((2 + -1x) + 2x * (-2 + x)) = 0 -5 + 9x + 2x2 + (2 + -1x + (-2 * 2x + x * 2x)) = 0 -5 + 9x + 2x2 + (2 + -1x + (-4x + 2x2)) = 0 Combine like terms: -1x + -4x = -5x -5 + 9x + 2x2 + (2 + -5x + 2x2) = 0 Reorder the terms: -5 + 2 + 9x + -5x + 2x2 + 2x2 = 0 Combine like terms: -5 + 2 = -3 -3 + 9x + -5x + 2x2 + 2x2 = 0 Combine like terms: 9x + -5x = 4x -3 + 4x + 2x2 + 2x2 = 0 Combine like terms: 2x2 + 2x2 = 4x2 -3 + 4x + 4x2 = 0 Solving -3 + 4x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(1 + -2x) = 0Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, 0.5}
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