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Simplifying 23x2 + -34x = -12 + 2x + -4x2 Reorder the terms: -34x + 23x2 = -12 + 2x + -4x2 Solving -34x + 23x2 = -12 + 2x + -4x2 Solving for variable 'x'. Reorder the terms: 12 + -34x + -2x + 23x2 + 4x2 = -12 + 2x + -4x2 + 12 + -2x + 4x2 Combine like terms: -34x + -2x = -36x 12 + -36x + 23x2 + 4x2 = -12 + 2x + -4x2 + 12 + -2x + 4x2 Combine like terms: 23x2 + 4x2 = 27x2 12 + -36x + 27x2 = -12 + 2x + -4x2 + 12 + -2x + 4x2 Reorder the terms: 12 + -36x + 27x2 = -12 + 12 + 2x + -2x + -4x2 + 4x2 Combine like terms: -12 + 12 = 0 12 + -36x + 27x2 = 0 + 2x + -2x + -4x2 + 4x2 12 + -36x + 27x2 = 2x + -2x + -4x2 + 4x2 Combine like terms: 2x + -2x = 0 12 + -36x + 27x2 = 0 + -4x2 + 4x2 12 + -36x + 27x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 12 + -36x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -12x + 9x2) = 0 Factor a trinomial. 3((2 + -3x)(2 + -3x)) = 0 Ignore the factor 3.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 '(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 = {0.6666666667, 0.6666666667}
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