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Simplifying (2x + -1)(1 + -2x) = 0 Reorder the terms: (-1 + 2x)(1 + -2x) = 0 Multiply (-1 + 2x) * (1 + -2x) (-1(1 + -2x) + 2x * (1 + -2x)) = 0 ((1 * -1 + -2x * -1) + 2x * (1 + -2x)) = 0 ((-1 + 2x) + 2x * (1 + -2x)) = 0 (-1 + 2x + (1 * 2x + -2x * 2x)) = 0 (-1 + 2x + (2x + -4x2)) = 0 Combine like terms: 2x + 2x = 4x (-1 + 4x + -4x2) = 0 Solving -1 + 4x + -4x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + 2x)(1 + -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 '(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 = {0.5, 0.5}
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