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Simplifying (x + -1) + -1(5 + -1x)(x + -1) = 0 Reorder the terms: (-1 + x) + -1(5 + -1x)(x + -1) = 0 Remove parenthesis around (-1 + x) -1 + x + -1(5 + -1x)(x + -1) = 0 Reorder the terms: -1 + x + -1(5 + -1x)(-1 + x) = 0 Multiply (5 + -1x) * (-1 + x) -1 + x + -1(5(-1 + x) + -1x * (-1 + x)) = 0 -1 + x + -1((-1 * 5 + x * 5) + -1x * (-1 + x)) = 0 -1 + x + -1((-5 + 5x) + -1x * (-1 + x)) = 0 -1 + x + -1(-5 + 5x + (-1 * -1x + x * -1x)) = 0 -1 + x + -1(-5 + 5x + (1x + -1x2)) = 0 Combine like terms: 5x + 1x = 6x -1 + x + -1(-5 + 6x + -1x2) = 0 -1 + x + (-5 * -1 + 6x * -1 + -1x2 * -1) = 0 -1 + x + (5 + -6x + 1x2) = 0 Reorder the terms: -1 + 5 + x + -6x + 1x2 = 0 Combine like terms: -1 + 5 = 4 4 + x + -6x + 1x2 = 0 Combine like terms: x + -6x = -5x 4 + -5x + 1x2 = 0 Solving 4 + -5x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x)(4 + -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 '(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 = 4Solution
x = {1, 4}
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