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Simplifying (x + -1)(x + -1) * x = 0 Reorder the terms: (-1 + x)(x + -1) * x = 0 Reorder the terms: (-1 + x)(-1 + x) * x = 0 Reorder the terms for easier multiplication: x(-1 + x)(-1 + x) = 0 Multiply (-1 + x) * (-1 + x) x(-1(-1 + x) + x(-1 + x)) = 0 x((-1 * -1 + x * -1) + x(-1 + x)) = 0 x((1 + -1x) + x(-1 + x)) = 0 x(1 + -1x + (-1 * x + x * x)) = 0 x(1 + -1x + (-1x + x2)) = 0 Combine like terms: -1x + -1x = -2x x(1 + -2x + x2) = 0 (1 * x + -2x * x + x2 * x) = 0 (1x + -2x2 + x3) = 0 Solving 1x + -2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -2x + x2) = 0 Factor a trinomial. x((1 + -1x)(1 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1, 1}
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