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Simplifying (1 + -1x)(8x + -4) = 0 Reorder the terms: (1 + -1x)(-4 + 8x) = 0 Multiply (1 + -1x) * (-4 + 8x) (1(-4 + 8x) + -1x * (-4 + 8x)) = 0 ((-4 * 1 + 8x * 1) + -1x * (-4 + 8x)) = 0 ((-4 + 8x) + -1x * (-4 + 8x)) = 0 (-4 + 8x + (-4 * -1x + 8x * -1x)) = 0 (-4 + 8x + (4x + -8x2)) = 0 Combine like terms: 8x + 4x = 12x (-4 + 12x + -8x2) = 0 Solving -4 + 12x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 3x + -2x2) = 0 Factor a trinomial. 4((-1 + x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 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, 0.5}
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