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Simplifying 22x + 27x2 = 54 + -5x Solving 22x + 27x2 = 54 + -5x Solving for variable 'x'. Reorder the terms: -54 + 22x + 5x + 27x2 = 54 + -5x + -54 + 5x Combine like terms: 22x + 5x = 27x -54 + 27x + 27x2 = 54 + -5x + -54 + 5x Reorder the terms: -54 + 27x + 27x2 = 54 + -54 + -5x + 5x Combine like terms: 54 + -54 = 0 -54 + 27x + 27x2 = 0 + -5x + 5x -54 + 27x + 27x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -54 + 27x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '27'. 27(-2 + x + x2) = 0 Factor a trinomial. 27((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 27.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 1}
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