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Simplifying (4x + 7)(4x + -1) = 0 Reorder the terms: (7 + 4x)(4x + -1) = 0 Reorder the terms: (7 + 4x)(-1 + 4x) = 0 Multiply (7 + 4x) * (-1 + 4x) (7(-1 + 4x) + 4x * (-1 + 4x)) = 0 ((-1 * 7 + 4x * 7) + 4x * (-1 + 4x)) = 0 ((-7 + 28x) + 4x * (-1 + 4x)) = 0 (-7 + 28x + (-1 * 4x + 4x * 4x)) = 0 (-7 + 28x + (-4x + 16x2)) = 0 Combine like terms: 28x + -4x = 24x (-7 + 24x + 16x2) = 0 Solving -7 + 24x + 16x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -4x)(1 + -4x) = 0Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75Subproblem 2
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 = 0.25Solution
x = {-1.75, 0.25}
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