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Simplifying (x2 + -1)(1 + -4x2) = 0 Reorder the terms: (-1 + x2)(1 + -4x2) = 0 Multiply (-1 + x2) * (1 + -4x2) (-1(1 + -4x2) + x2(1 + -4x2)) = 0 ((1 * -1 + -4x2 * -1) + x2(1 + -4x2)) = 0 ((-1 + 4x2) + x2(1 + -4x2)) = 0 (-1 + 4x2 + (1 * x2 + -4x2 * x2)) = 0 (-1 + 4x2 + (1x2 + -4x4)) = 0 Combine like terms: 4x2 + 1x2 = 5x2 (-1 + 5x2 + -4x4) = 0 Solving -1 + 5x2 + -4x4 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + x2)(1 + -4x2) = 0 Factor a difference between two squares. ((1 + x)(-1 + x))(1 + -4x2) = 0 Factor a difference between two squares. ((1 + 2x)(1 + -2x))(1 + x)(-1 + x) = 0Subproblem 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 + 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 3
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 4
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, 1, -0.5, 0.5}
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