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Simplifying (4X + 1)(2X + 7) = 0 Reorder the terms: (1 + 4X)(2X + 7) = 0 Reorder the terms: (1 + 4X)(7 + 2X) = 0 Multiply (1 + 4X) * (7 + 2X) (1(7 + 2X) + 4X * (7 + 2X)) = 0 ((7 * 1 + 2X * 1) + 4X * (7 + 2X)) = 0 ((7 + 2X) + 4X * (7 + 2X)) = 0 (7 + 2X + (7 * 4X + 2X * 4X)) = 0 (7 + 2X + (28X + 8X2)) = 0 Combine like terms: 2X + 28X = 30X (7 + 30X + 8X2) = 0 Solving 7 + 30X + 8X2 = 0 Solving for variable 'X'. Factor a trinomial. (7 + 2X)(1 + 4X) = 0Subproblem 1
Set the factor '(7 + 2X)' equal to zero and attempt to solve: Simplifying 7 + 2X = 0 Solving 7 + 2X = 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 + 2X = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2X = 0 + -7 2X = 0 + -7 Combine like terms: 0 + -7 = -7 2X = -7 Divide each side by '2'. X = -3.5 Simplifying X = -3.5Subproblem 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 = {-3.5, -0.25}
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