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Simplifying (5a + -7)(2a + 5) = 0 Reorder the terms: (-7 + 5a)(2a + 5) = 0 Reorder the terms: (-7 + 5a)(5 + 2a) = 0 Multiply (-7 + 5a) * (5 + 2a) (-7(5 + 2a) + 5a * (5 + 2a)) = 0 ((5 * -7 + 2a * -7) + 5a * (5 + 2a)) = 0 ((-35 + -14a) + 5a * (5 + 2a)) = 0 (-35 + -14a + (5 * 5a + 2a * 5a)) = 0 (-35 + -14a + (25a + 10a2)) = 0 Combine like terms: -14a + 25a = 11a (-35 + 11a + 10a2) = 0 Solving -35 + 11a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -2a)(7 + -5a) = 0Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 2
Set the factor '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 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 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4Solution
a = {-2.5, 1.4}
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