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Simplifying (2x + -1)(4 + -1x) = 0 Reorder the terms: (-1 + 2x)(4 + -1x) = 0 Multiply (-1 + 2x) * (4 + -1x) (-1(4 + -1x) + 2x * (4 + -1x)) = 0 ((4 * -1 + -1x * -1) + 2x * (4 + -1x)) = 0 ((-4 + 1x) + 2x * (4 + -1x)) = 0 (-4 + 1x + (4 * 2x + -1x * 2x)) = 0 (-4 + 1x + (8x + -2x2)) = 0 Combine like terms: 1x + 8x = 9x (-4 + 9x + -2x2) = 0 Solving -4 + 9x + -2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-4 + x)(1 + -2x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 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 = {4, 0.5}
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