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Simplifying 18x2 + 42x + -6 = 10 Reorder the terms: -6 + 42x + 18x2 = 10 Solving -6 + 42x + 18x2 = 10 Solving for variable 'x'. Reorder the terms: -6 + -10 + 42x + 18x2 = 10 + -10 Combine like terms: -6 + -10 = -16 -16 + 42x + 18x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -16 + 42x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 21x + 9x2) = 0 Factor a trinomial. 2((-8 + -3x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve: Simplifying -8 + -3x = 0 Solving -8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x = 0 + 8 -3x = 0 + 8 Combine like terms: 0 + 8 = 8 -3x = 8 Divide each side by '-3'. x = -2.666666667 Simplifying x = -2.666666667Subproblem 2
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 = 0.3333333333Solution
x = {-2.666666667, 0.3333333333}
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