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Simplifying (8X + 1)(16X + -13) = 0 Reorder the terms: (1 + 8X)(16X + -13) = 0 Reorder the terms: (1 + 8X)(-13 + 16X) = 0 Multiply (1 + 8X) * (-13 + 16X) (1(-13 + 16X) + 8X * (-13 + 16X)) = 0 ((-13 * 1 + 16X * 1) + 8X * (-13 + 16X)) = 0 ((-13 + 16X) + 8X * (-13 + 16X)) = 0 (-13 + 16X + (-13 * 8X + 16X * 8X)) = 0 (-13 + 16X + (-104X + 128X2)) = 0 Combine like terms: 16X + -104X = -88X (-13 + -88X + 128X2) = 0 Solving -13 + -88X + 128X2 = 0 Solving for variable 'X'. Factor a trinomial. (-1 + -8X)(13 + -16X) = 0Subproblem 1
Set the factor '(-1 + -8X)' equal to zero and attempt to solve: Simplifying -1 + -8X = 0 Solving -1 + -8X = 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 + -8X = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8X = 0 + 1 -8X = 0 + 1 Combine like terms: 0 + 1 = 1 -8X = 1 Divide each side by '-8'. X = -0.125 Simplifying X = -0.125Subproblem 2
Set the factor '(13 + -16X)' equal to zero and attempt to solve: Simplifying 13 + -16X = 0 Solving 13 + -16X = 0 Move all terms containing X to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -16X = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -16X = 0 + -13 -16X = 0 + -13 Combine like terms: 0 + -13 = -13 -16X = -13 Divide each side by '-16'. X = 0.8125 Simplifying X = 0.8125Solution
X = {-0.125, 0.8125}
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