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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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