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Simplifying (2a + -1)(4a + -7) = 0 Reorder the terms: (-1 + 2a)(4a + -7) = 0 Reorder the terms: (-1 + 2a)(-7 + 4a) = 0 Multiply (-1 + 2a) * (-7 + 4a) (-1(-7 + 4a) + 2a * (-7 + 4a)) = 0 ((-7 * -1 + 4a * -1) + 2a * (-7 + 4a)) = 0 ((7 + -4a) + 2a * (-7 + 4a)) = 0 (7 + -4a + (-7 * 2a + 4a * 2a)) = 0 (7 + -4a + (-14a + 8a2)) = 0 Combine like terms: -4a + -14a = -18a (7 + -18a + 8a2) = 0 Solving 7 + -18a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a)(7 + -4a) = 0Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {0.5, 1.75}
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