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Simplifying (4x + 1)(x + -8) = 0 Reorder the terms: (1 + 4x)(x + -8) = 0 Reorder the terms: (1 + 4x)(-8 + x) = 0 Multiply (1 + 4x) * (-8 + x) (1(-8 + x) + 4x * (-8 + x)) = 0 ((-8 * 1 + x * 1) + 4x * (-8 + x)) = 0 ((-8 + 1x) + 4x * (-8 + x)) = 0 (-8 + 1x + (-8 * 4x + x * 4x)) = 0 (-8 + 1x + (-32x + 4x2)) = 0 Combine like terms: 1x + -32x = -31x (-8 + -31x + 4x2) = 0 Solving -8 + -31x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -4x)(8 + -1x) = 0Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-0.25, 8}
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