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Simplifying 12x2 + 18x + 34 = 37 + 2x Reorder the terms: 34 + 18x + 12x2 = 37 + 2x Solving 34 + 18x + 12x2 = 37 + 2x Solving for variable 'x'. Reorder the terms: 34 + -37 + 18x + -2x + 12x2 = 37 + 2x + -37 + -2x Combine like terms: 34 + -37 = -3 -3 + 18x + -2x + 12x2 = 37 + 2x + -37 + -2x Combine like terms: 18x + -2x = 16x -3 + 16x + 12x2 = 37 + 2x + -37 + -2x Reorder the terms: -3 + 16x + 12x2 = 37 + -37 + 2x + -2x Combine like terms: 37 + -37 = 0 -3 + 16x + 12x2 = 0 + 2x + -2x -3 + 16x + 12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -3 + 16x + 12x2 = 0 Factor a trinomial. (-3 + -2x)(1 + -6x) = 0Subproblem 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 '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 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 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Divide each side by '-6'. x = 0.1666666667 Simplifying x = 0.1666666667Solution
x = {-1.5, 0.1666666667}
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