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Simplifying (7x + -7)(1 + -1x) = 0 Reorder the terms: (-7 + 7x)(1 + -1x) = 0 Multiply (-7 + 7x) * (1 + -1x) (-7(1 + -1x) + 7x * (1 + -1x)) = 0 ((1 * -7 + -1x * -7) + 7x * (1 + -1x)) = 0 ((-7 + 7x) + 7x * (1 + -1x)) = 0 (-7 + 7x + (1 * 7x + -1x * 7x)) = 0 (-7 + 7x + (7x + -7x2)) = 0 Combine like terms: 7x + 7x = 14x (-7 + 14x + -7x2) = 0 Solving -7 + 14x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-1 + 2x + -1x2) = 0 Factor a trinomial. 7((-1 + x)(1 + -1x)) = 0 Ignore the factor 7.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 + -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 = {1, 1}
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