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Simplifying 0 = -64x2 + -384x + -176 Reorder the terms: 0 = -176 + -384x + -64x2 Solving 0 = -176 + -384x + -64x2 Solving for variable 'x'. Combine like terms: 0 + 176 = 176 176 + 384x + 64x2 = -176 + -384x + -64x2 + 176 + 384x + 64x2 Reorder the terms: 176 + 384x + 64x2 = -176 + 176 + -384x + 384x + -64x2 + 64x2 Combine like terms: -176 + 176 = 0 176 + 384x + 64x2 = 0 + -384x + 384x + -64x2 + 64x2 176 + 384x + 64x2 = -384x + 384x + -64x2 + 64x2 Combine like terms: -384x + 384x = 0 176 + 384x + 64x2 = 0 + -64x2 + 64x2 176 + 384x + 64x2 = -64x2 + 64x2 Combine like terms: -64x2 + 64x2 = 0 176 + 384x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(11 + 24x + 4x2) = 0 Factor a trinomial. 16((11 + 2x)(1 + 2x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(11 + 2x)' equal to zero and attempt to solve: Simplifying 11 + 2x = 0 Solving 11 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2x = 0 + -11 2x = 0 + -11 Combine like terms: 0 + -11 = -11 2x = -11 Divide each side by '2'. x = -5.5 Simplifying x = -5.5Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-5.5, -0.5}
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