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Simplifying 0 = 3x2 + 14x + 16 Reorder the terms: 0 = 16 + 14x + 3x2 Solving 0 = 16 + 14x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -14x + -3x2 = 16 + 14x + 3x2 + -16 + -14x + -3x2 Reorder the terms: -16 + -14x + -3x2 = 16 + -16 + 14x + -14x + 3x2 + -3x2 Combine like terms: 16 + -16 = 0 -16 + -14x + -3x2 = 0 + 14x + -14x + 3x2 + -3x2 -16 + -14x + -3x2 = 14x + -14x + 3x2 + -3x2 Combine like terms: 14x + -14x = 0 -16 + -14x + -3x2 = 0 + 3x2 + -3x2 -16 + -14x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -16 + -14x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 14x + 3x2) = 0 Factor a trinomial. -1((8 + 3x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 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 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Divide each side by '3'. x = -2.666666667 Simplifying x = -2.666666667Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2.666666667, -2}
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