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Simplifying -12x2 + -24x = 9 Reorder the terms: -24x + -12x2 = 9 Solving -24x + -12x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -24x + -12x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -24x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(3 + 8x + 4x2) = 0 Factor a trinomial. -3((3 + 2x)(1 + 2x)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.5, -0.5}
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