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Simplifying -6 = -6x2 + -9x + 9 Reorder the terms: -6 = 9 + -9x + -6x2 Solving -6 = 9 + -9x + -6x2 Solving for variable 'x'. Combine like terms: -6 + -9 = -15 -15 + 9x + 6x2 = 9 + -9x + -6x2 + -9 + 9x + 6x2 Reorder the terms: -15 + 9x + 6x2 = 9 + -9 + -9x + 9x + -6x2 + 6x2 Combine like terms: 9 + -9 = 0 -15 + 9x + 6x2 = 0 + -9x + 9x + -6x2 + 6x2 -15 + 9x + 6x2 = -9x + 9x + -6x2 + 6x2 Combine like terms: -9x + 9x = 0 -15 + 9x + 6x2 = 0 + -6x2 + 6x2 -15 + 9x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -15 + 9x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3x + 2x2) = 0 Factor a trinomial. 3((-5 + -2x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -2.5Subproblem 2
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 = 1Solution
x = {-2.5, 1}
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