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Simplifying 0 = 16x2 + 24x + -216 Reorder the terms: 0 = -216 + 24x + 16x2 Solving 0 = -216 + 24x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 216 = 216 216 + -24x + -16x2 = -216 + 24x + 16x2 + 216 + -24x + -16x2 Reorder the terms: 216 + -24x + -16x2 = -216 + 216 + 24x + -24x + 16x2 + -16x2 Combine like terms: -216 + 216 = 0 216 + -24x + -16x2 = 0 + 24x + -24x + 16x2 + -16x2 216 + -24x + -16x2 = 24x + -24x + 16x2 + -16x2 Combine like terms: 24x + -24x = 0 216 + -24x + -16x2 = 0 + 16x2 + -16x2 216 + -24x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 216 + -24x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(27 + -3x + -2x2) = 0 Factor a trinomial. 8((3 + -1x)(9 + 2x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Solution
x = {3, -4.5}
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