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Simplifying 0 = 2X2 + 19X + 24 Reorder the terms: 0 = 24 + 19X + 2X2 Solving 0 = 24 + 19X + 2X2 Solving for variable 'X'. Combine like terms: 0 + -24 = -24 -24 + -19X + -2X2 = 24 + 19X + 2X2 + -24 + -19X + -2X2 Reorder the terms: -24 + -19X + -2X2 = 24 + -24 + 19X + -19X + 2X2 + -2X2 Combine like terms: 24 + -24 = 0 -24 + -19X + -2X2 = 0 + 19X + -19X + 2X2 + -2X2 -24 + -19X + -2X2 = 19X + -19X + 2X2 + -2X2 Combine like terms: 19X + -19X = 0 -24 + -19X + -2X2 = 0 + 2X2 + -2X2 -24 + -19X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 -24 + -19X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 19X + 2X2) = 0 Factor a trinomial. -1((8 + X)(3 + 2X)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + X)' equal to zero and attempt to solve: Simplifying 8 + X = 0 Solving 8 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + X = 0 + -8 Combine like terms: 8 + -8 = 0 0 + X = 0 + -8 X = 0 + -8 Combine like terms: 0 + -8 = -8 X = -8 Simplifying X = -8Subproblem 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 = {-8, -1.5}
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