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Simplifying (1 + -1x)(1 + -1x) + -4 = 0 Multiply (1 + -1x) * (1 + -1x) (1(1 + -1x) + -1x * (1 + -1x)) + -4 = 0 ((1 * 1 + -1x * 1) + -1x * (1 + -1x)) + -4 = 0 ((1 + -1x) + -1x * (1 + -1x)) + -4 = 0 (1 + -1x + (1 * -1x + -1x * -1x)) + -4 = 0 (1 + -1x + (-1x + 1x2)) + -4 = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + 1x2) + -4 = 0 Reorder the terms: 1 + -4 + -2x + 1x2 = 0 Combine like terms: 1 + -4 = -3 -3 + -2x + 1x2 = 0 Solving -3 + -2x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(3 + -1x) = 0Subproblem 1
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 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1, 3}
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