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Simplifying 27 + -5x2 + -4x = 2x + 23 + -7x2 Reorder the terms: 27 + -4x + -5x2 = 2x + 23 + -7x2 Reorder the terms: 27 + -4x + -5x2 = 23 + 2x + -7x2 Solving 27 + -4x + -5x2 = 23 + 2x + -7x2 Solving for variable 'x'. Reorder the terms: 27 + -23 + -4x + -2x + -5x2 + 7x2 = 23 + 2x + -7x2 + -23 + -2x + 7x2 Combine like terms: 27 + -23 = 4 4 + -4x + -2x + -5x2 + 7x2 = 23 + 2x + -7x2 + -23 + -2x + 7x2 Combine like terms: -4x + -2x = -6x 4 + -6x + -5x2 + 7x2 = 23 + 2x + -7x2 + -23 + -2x + 7x2 Combine like terms: -5x2 + 7x2 = 2x2 4 + -6x + 2x2 = 23 + 2x + -7x2 + -23 + -2x + 7x2 Reorder the terms: 4 + -6x + 2x2 = 23 + -23 + 2x + -2x + -7x2 + 7x2 Combine like terms: 23 + -23 = 0 4 + -6x + 2x2 = 0 + 2x + -2x + -7x2 + 7x2 4 + -6x + 2x2 = 2x + -2x + -7x2 + 7x2 Combine like terms: 2x + -2x = 0 4 + -6x + 2x2 = 0 + -7x2 + 7x2 4 + -6x + 2x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 4 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3x + x2) = 0 Factor a trinomial. 2((1 + -1x)(2 + -1x)) = 0 Ignore the factor 2.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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