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Simplifying -24 = 54x + -54x2 Solving -24 = 54x + -54x2 Solving for variable 'x'. Reorder the terms: -24 + -54x + 54x2 = 54x + -54x + -54x2 + 54x2 Combine like terms: 54x + -54x = 0 -24 + -54x + 54x2 = 0 + -54x2 + 54x2 -24 + -54x + 54x2 = -54x2 + 54x2 Combine like terms: -54x2 + 54x2 = 0 -24 + -54x + 54x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -9x + 9x2) = 0 Factor a trinomial. 6((-1 + -3x)(4 + -3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-0.3333333333, 1.333333333}
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