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Simplifying (1 + -1x)(1 + -1x) = 25 Multiply (1 + -1x) * (1 + -1x) (1(1 + -1x) + -1x * (1 + -1x)) = 25 ((1 * 1 + -1x * 1) + -1x * (1 + -1x)) = 25 ((1 + -1x) + -1x * (1 + -1x)) = 25 (1 + -1x + (1 * -1x + -1x * -1x)) = 25 (1 + -1x + (-1x + 1x2)) = 25 Combine like terms: -1x + -1x = -2x (1 + -2x + 1x2) = 25 Solving 1 + -2x + 1x2 = 25 Solving for variable 'x'. Reorder the terms: 1 + -25 + -2x + 1x2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + -2x + 1x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + -2x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-4, 6}
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