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Simplifying 2x + -1 = x2 + -4x + 4 Reorder the terms: -1 + 2x = x2 + -4x + 4 Reorder the terms: -1 + 2x = 4 + -4x + x2 Solving -1 + 2x = 4 + -4x + x2 Solving for variable 'x'. Reorder the terms: -1 + -4 + 2x + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Combine like terms: -1 + -4 = -5 -5 + 2x + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Combine like terms: 2x + 4x = 6x -5 + 6x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Reorder the terms: -5 + 6x + -1x2 = 4 + -4 + -4x + 4x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -5 + 6x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -5 + 6x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -5 + 6x + -1x2 = 0 + x2 + -1x2 -5 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5 + 6x + -1x2 = 0 Factor a trinomial. (-5 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 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 = {5, 1}
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