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Simplifying 0 = 16x2 + 64x + 60 Reorder the terms: 0 = 60 + 64x + 16x2 Solving 0 = 60 + 64x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -64x + -16x2 = 60 + 64x + 16x2 + -60 + -64x + -16x2 Reorder the terms: -60 + -64x + -16x2 = 60 + -60 + 64x + -64x + 16x2 + -16x2 Combine like terms: 60 + -60 = 0 -60 + -64x + -16x2 = 0 + 64x + -64x + 16x2 + -16x2 -60 + -64x + -16x2 = 64x + -64x + 16x2 + -16x2 Combine like terms: 64x + -64x = 0 -60 + -64x + -16x2 = 0 + 16x2 + -16x2 -60 + -64x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -60 + -64x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(15 + 16x + 4x2) = 0 Factor a trinomial. -4((5 + 2x)(3 + 2x)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, -1.5}
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