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Simplifying 0 = 8x2 + 24x + 18 Reorder the terms: 0 = 18 + 24x + 8x2 Solving 0 = 18 + 24x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + -24x + -8x2 = 18 + 24x + 8x2 + -18 + -24x + -8x2 Reorder the terms: -18 + -24x + -8x2 = 18 + -18 + 24x + -24x + 8x2 + -8x2 Combine like terms: 18 + -18 = 0 -18 + -24x + -8x2 = 0 + 24x + -24x + 8x2 + -8x2 -18 + -24x + -8x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 -18 + -24x + -8x2 = 0 + 8x2 + -8x2 -18 + -24x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -18 + -24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 12x + 4x2) = 0 Factor a trinomial. -2((3 + 2x)(3 + 2x)) = 0 Ignore the factor -2.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 '(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 = -1.5Solution
x = {-1.5, -1.5}
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