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Simplifying 54x2 + 45x = 54 Reorder the terms: 45x + 54x2 = 54 Solving 45x + 54x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 45x + 54x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 45x + 54x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-6 + 5x + 6x2) = 0 Factor a trinomial. 9((-3 + -2x)(2 + -3x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-1.5, 0.6666666667}
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