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Simplifying 4x2 = 12 + -22x Solving 4x2 = 12 + -22x Solving for variable 'x'. Reorder the terms: -12 + 22x + 4x2 = 12 + -22x + -12 + 22x Reorder the terms: -12 + 22x + 4x2 = 12 + -12 + -22x + 22x Combine like terms: 12 + -12 = 0 -12 + 22x + 4x2 = 0 + -22x + 22x -12 + 22x + 4x2 = -22x + 22x Combine like terms: -22x + 22x = 0 -12 + 22x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 11x + 2x2) = 0 Factor a trinomial. 2((-6 + -1x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-6, 0.5}
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