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Simplifying 3x2 + -7x + 4 = x2 + 3x + -8 Reorder the terms: 4 + -7x + 3x2 = x2 + 3x + -8 Reorder the terms: 4 + -7x + 3x2 = -8 + 3x + x2 Solving 4 + -7x + 3x2 = -8 + 3x + x2 Solving for variable 'x'. Reorder the terms: 4 + 8 + -7x + -3x + 3x2 + -1x2 = -8 + 3x + x2 + 8 + -3x + -1x2 Combine like terms: 4 + 8 = 12 12 + -7x + -3x + 3x2 + -1x2 = -8 + 3x + x2 + 8 + -3x + -1x2 Combine like terms: -7x + -3x = -10x 12 + -10x + 3x2 + -1x2 = -8 + 3x + x2 + 8 + -3x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 12 + -10x + 2x2 = -8 + 3x + x2 + 8 + -3x + -1x2 Reorder the terms: 12 + -10x + 2x2 = -8 + 8 + 3x + -3x + x2 + -1x2 Combine like terms: -8 + 8 = 0 12 + -10x + 2x2 = 0 + 3x + -3x + x2 + -1x2 12 + -10x + 2x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 12 + -10x + 2x2 = 0 + x2 + -1x2 12 + -10x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5x + x2) = 0 Factor a trinomial. 2((2 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {2, 3}
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