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Simplifying -1x + 4 = -1x2 + 5x + -1 Reorder the terms: 4 + -1x = -1x2 + 5x + -1 Reorder the terms: 4 + -1x = -1 + 5x + -1x2 Solving 4 + -1x = -1 + 5x + -1x2 Solving for variable 'x'. Reorder the terms: 4 + 1 + -1x + -5x + x2 = -1 + 5x + -1x2 + 1 + -5x + x2 Combine like terms: 4 + 1 = 5 5 + -1x + -5x + x2 = -1 + 5x + -1x2 + 1 + -5x + x2 Combine like terms: -1x + -5x = -6x 5 + -6x + x2 = -1 + 5x + -1x2 + 1 + -5x + x2 Reorder the terms: 5 + -6x + x2 = -1 + 1 + 5x + -5x + -1x2 + x2 Combine like terms: -1 + 1 = 0 5 + -6x + x2 = 0 + 5x + -5x + -1x2 + x2 5 + -6x + x2 = 5x + -5x + -1x2 + x2 Combine like terms: 5x + -5x = 0 5 + -6x + x2 = 0 + -1x2 + x2 5 + -6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5 + -6x + x2 = 0 Factor a trinomial. (1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {1, 5}
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