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Simplifying (4x + 1)(7x + -1) = 0 Reorder the terms: (1 + 4x)(7x + -1) = 0 Reorder the terms: (1 + 4x)(-1 + 7x) = 0 Multiply (1 + 4x) * (-1 + 7x) (1(-1 + 7x) + 4x * (-1 + 7x)) = 0 ((-1 * 1 + 7x * 1) + 4x * (-1 + 7x)) = 0 ((-1 + 7x) + 4x * (-1 + 7x)) = 0 (-1 + 7x + (-1 * 4x + 7x * 4x)) = 0 (-1 + 7x + (-4x + 28x2)) = 0 Combine like terms: 7x + -4x = 3x (-1 + 3x + 28x2) = 0 Solving -1 + 3x + 28x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -4x)(1 + -7x) = 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 '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Solution
x = {-0.25, 0.1428571429}
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