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Simplifying -13 + -9x = -8x2 + 3x + 7 Reorder the terms: -13 + -9x = 7 + 3x + -8x2 Solving -13 + -9x = 7 + 3x + -8x2 Solving for variable 'x'. Reorder the terms: -13 + -7 + -9x + -3x + 8x2 = 7 + 3x + -8x2 + -7 + -3x + 8x2 Combine like terms: -13 + -7 = -20 -20 + -9x + -3x + 8x2 = 7 + 3x + -8x2 + -7 + -3x + 8x2 Combine like terms: -9x + -3x = -12x -20 + -12x + 8x2 = 7 + 3x + -8x2 + -7 + -3x + 8x2 Reorder the terms: -20 + -12x + 8x2 = 7 + -7 + 3x + -3x + -8x2 + 8x2 Combine like terms: 7 + -7 = 0 -20 + -12x + 8x2 = 0 + 3x + -3x + -8x2 + 8x2 -20 + -12x + 8x2 = 3x + -3x + -8x2 + 8x2 Combine like terms: 3x + -3x = 0 -20 + -12x + 8x2 = 0 + -8x2 + 8x2 -20 + -12x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -20 + -12x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -3x + 2x2) = 0 Factor a trinomial. 4((-1 + -1x)(5 + -2x)) = 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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-1, 2.5}
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