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Simplifying 9 + 19x = -18x2 + x + 5 Reorder the terms: 9 + 19x = 5 + x + -18x2 Solving 9 + 19x = 5 + x + -18x2 Solving for variable 'x'. Reorder the terms: 9 + -5 + 19x + -1x + 18x2 = 5 + x + -18x2 + -5 + -1x + 18x2 Combine like terms: 9 + -5 = 4 4 + 19x + -1x + 18x2 = 5 + x + -18x2 + -5 + -1x + 18x2 Combine like terms: 19x + -1x = 18x 4 + 18x + 18x2 = 5 + x + -18x2 + -5 + -1x + 18x2 Reorder the terms: 4 + 18x + 18x2 = 5 + -5 + x + -1x + -18x2 + 18x2 Combine like terms: 5 + -5 = 0 4 + 18x + 18x2 = 0 + x + -1x + -18x2 + 18x2 4 + 18x + 18x2 = x + -1x + -18x2 + 18x2 Combine like terms: x + -1x = 0 4 + 18x + 18x2 = 0 + -18x2 + 18x2 4 + 18x + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 4 + 18x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 9x + 9x2) = 0 Factor a trinomial. 2((2 + 3x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.6666666667Subproblem 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 = {-0.6666666667, -0.3333333333}
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