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Simplifying 2x2 + -5x + 3 = -2x2 + -1x + 11 Reorder the terms: 3 + -5x + 2x2 = -2x2 + -1x + 11 Reorder the terms: 3 + -5x + 2x2 = 11 + -1x + -2x2 Solving 3 + -5x + 2x2 = 11 + -1x + -2x2 Solving for variable 'x'. Reorder the terms: 3 + -11 + -5x + x + 2x2 + 2x2 = 11 + -1x + -2x2 + -11 + x + 2x2 Combine like terms: 3 + -11 = -8 -8 + -5x + x + 2x2 + 2x2 = 11 + -1x + -2x2 + -11 + x + 2x2 Combine like terms: -5x + x = -4x -8 + -4x + 2x2 + 2x2 = 11 + -1x + -2x2 + -11 + x + 2x2 Combine like terms: 2x2 + 2x2 = 4x2 -8 + -4x + 4x2 = 11 + -1x + -2x2 + -11 + x + 2x2 Reorder the terms: -8 + -4x + 4x2 = 11 + -11 + -1x + x + -2x2 + 2x2 Combine like terms: 11 + -11 = 0 -8 + -4x + 4x2 = 0 + -1x + x + -2x2 + 2x2 -8 + -4x + 4x2 = -1x + x + -2x2 + 2x2 Combine like terms: -1x + x = 0 -8 + -4x + 4x2 = 0 + -2x2 + 2x2 -8 + -4x + 4x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -8 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -1x + x2) = 0 Factor a trinomial. 4((-1 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = -1Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1, 2}
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