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Simplifying 0 = (2x + 3)(8 + 11x) Reorder the terms: 0 = (3 + 2x)(8 + 11x) Multiply (3 + 2x) * (8 + 11x) 0 = (3(8 + 11x) + 2x * (8 + 11x)) 0 = ((8 * 3 + 11x * 3) + 2x * (8 + 11x)) 0 = ((24 + 33x) + 2x * (8 + 11x)) 0 = (24 + 33x + (8 * 2x + 11x * 2x)) 0 = (24 + 33x + (16x + 22x2)) Combine like terms: 33x + 16x = 49x 0 = (24 + 49x + 22x2) Solving 0 = 24 + 49x + 22x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -49x + -22x2 = 24 + 49x + 22x2 + -24 + -49x + -22x2 Reorder the terms: -24 + -49x + -22x2 = 24 + -24 + 49x + -49x + 22x2 + -22x2 Combine like terms: 24 + -24 = 0 -24 + -49x + -22x2 = 0 + 49x + -49x + 22x2 + -22x2 -24 + -49x + -22x2 = 49x + -49x + 22x2 + -22x2 Combine like terms: 49x + -49x = 0 -24 + -49x + -22x2 = 0 + 22x2 + -22x2 -24 + -49x + -22x2 = 22x2 + -22x2 Combine like terms: 22x2 + -22x2 = 0 -24 + -49x + -22x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 49x + 22x2) = 0 Factor a trinomial. -1((3 + 2x)(8 + 11x)) = 0 Ignore the factor -1.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 '(8 + 11x)' equal to zero and attempt to solve: Simplifying 8 + 11x = 0 Solving 8 + 11x = 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 + 11x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 11x = 0 + -8 11x = 0 + -8 Combine like terms: 0 + -8 = -8 11x = -8 Divide each side by '11'. x = -0.7272727273 Simplifying x = -0.7272727273Solution
x = {-1.5, -0.7272727273}
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