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Simplifying x2 + -24x = -22x + 24 + -1x2 Reorder the terms: -24x + x2 = -22x + 24 + -1x2 Reorder the terms: -24x + x2 = 24 + -22x + -1x2 Solving -24x + x2 = 24 + -22x + -1x2 Solving for variable 'x'. Reorder the terms: -24 + -24x + 22x + x2 + x2 = 24 + -22x + -1x2 + -24 + 22x + x2 Combine like terms: -24x + 22x = -2x -24 + -2x + x2 + x2 = 24 + -22x + -1x2 + -24 + 22x + x2 Combine like terms: x2 + x2 = 2x2 -24 + -2x + 2x2 = 24 + -22x + -1x2 + -24 + 22x + x2 Reorder the terms: -24 + -2x + 2x2 = 24 + -24 + -22x + 22x + -1x2 + x2 Combine like terms: 24 + -24 = 0 -24 + -2x + 2x2 = 0 + -22x + 22x + -1x2 + x2 -24 + -2x + 2x2 = -22x + 22x + -1x2 + x2 Combine like terms: -22x + 22x = 0 -24 + -2x + 2x2 = 0 + -1x2 + x2 -24 + -2x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -24 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -1x + x2) = 0 Factor a trinomial. 2((-3 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 4}
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