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Simplifying x2 + 6x + -2 = -2x2 + -12x + 19 Reorder the terms: -2 + 6x + x2 = -2x2 + -12x + 19 Reorder the terms: -2 + 6x + x2 = 19 + -12x + -2x2 Solving -2 + 6x + x2 = 19 + -12x + -2x2 Solving for variable 'x'. Reorder the terms: -2 + -19 + 6x + 12x + x2 + 2x2 = 19 + -12x + -2x2 + -19 + 12x + 2x2 Combine like terms: -2 + -19 = -21 -21 + 6x + 12x + x2 + 2x2 = 19 + -12x + -2x2 + -19 + 12x + 2x2 Combine like terms: 6x + 12x = 18x -21 + 18x + x2 + 2x2 = 19 + -12x + -2x2 + -19 + 12x + 2x2 Combine like terms: x2 + 2x2 = 3x2 -21 + 18x + 3x2 = 19 + -12x + -2x2 + -19 + 12x + 2x2 Reorder the terms: -21 + 18x + 3x2 = 19 + -19 + -12x + 12x + -2x2 + 2x2 Combine like terms: 19 + -19 = 0 -21 + 18x + 3x2 = 0 + -12x + 12x + -2x2 + 2x2 -21 + 18x + 3x2 = -12x + 12x + -2x2 + 2x2 Combine like terms: -12x + 12x = 0 -21 + 18x + 3x2 = 0 + -2x2 + 2x2 -21 + 18x + 3x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -21 + 18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 6x + x2) = 0 Factor a trinomial. 3((-7 + -1x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-7, 1}
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