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Simplifying (4x + 1)(2x + -1) = 0 Reorder the terms: (1 + 4x)(2x + -1) = 0 Reorder the terms: (1 + 4x)(-1 + 2x) = 0 Multiply (1 + 4x) * (-1 + 2x) (1(-1 + 2x) + 4x * (-1 + 2x)) = 0 ((-1 * 1 + 2x * 1) + 4x * (-1 + 2x)) = 0 ((-1 + 2x) + 4x * (-1 + 2x)) = 0 (-1 + 2x + (-1 * 4x + 2x * 4x)) = 0 (-1 + 2x + (-4x + 8x2)) = 0 Combine like terms: 2x + -4x = -2x (-1 + -2x + 8x2) = 0 Solving -1 + -2x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -4x)(1 + -2x) = 0Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 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 = {-0.25, 0.5}
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