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Simplifying 0 = 9x2 + 18x + 5 Reorder the terms: 0 = 5 + 18x + 9x2 Solving 0 = 5 + 18x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -18x + -9x2 = 5 + 18x + 9x2 + -5 + -18x + -9x2 Reorder the terms: -5 + -18x + -9x2 = 5 + -5 + 18x + -18x + 9x2 + -9x2 Combine like terms: 5 + -5 = 0 -5 + -18x + -9x2 = 0 + 18x + -18x + 9x2 + -9x2 -5 + -18x + -9x2 = 18x + -18x + 9x2 + -9x2 Combine like terms: 18x + -18x = 0 -5 + -18x + -9x2 = 0 + 9x2 + -9x2 -5 + -18x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -5 + -18x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 18x + 9x2) = 0 Factor a trinomial. -1((5 + 3x)(1 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 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 = {-1.666666667, -0.3333333333}
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