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Simplifying 3x + 9 + -2x2 + -6x = 6x2 + 2x + -3x + -1 Reorder the terms: 9 + 3x + -6x + -2x2 = 6x2 + 2x + -3x + -1 Combine like terms: 3x + -6x = -3x 9 + -3x + -2x2 = 6x2 + 2x + -3x + -1 Reorder the terms: 9 + -3x + -2x2 = -1 + 2x + -3x + 6x2 Combine like terms: 2x + -3x = -1x 9 + -3x + -2x2 = -1 + -1x + 6x2 Solving 9 + -3x + -2x2 = -1 + -1x + 6x2 Solving for variable 'x'. Reorder the terms: 9 + 1 + -3x + x + -2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: 9 + 1 = 10 10 + -3x + x + -2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: -3x + x = -2x 10 + -2x + -2x2 + -6x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Combine like terms: -2x2 + -6x2 = -8x2 10 + -2x + -8x2 = -1 + -1x + 6x2 + 1 + x + -6x2 Reorder the terms: 10 + -2x + -8x2 = -1 + 1 + -1x + x + 6x2 + -6x2 Combine like terms: -1 + 1 = 0 10 + -2x + -8x2 = 0 + -1x + x + 6x2 + -6x2 10 + -2x + -8x2 = -1x + x + 6x2 + -6x2 Combine like terms: -1x + x = 0 10 + -2x + -8x2 = 0 + 6x2 + -6x2 10 + -2x + -8x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 10 + -2x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -1x + -4x2) = 0 Factor a trinomial. 2((1 + -1x)(5 + 4x)) = 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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Solution
x = {1, -1.25}
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