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Simplifying 7(2a + 1)(7a + -5) = 0 Reorder the terms: 7(1 + 2a)(7a + -5) = 0 Reorder the terms: 7(1 + 2a)(-5 + 7a) = 0 Multiply (1 + 2a) * (-5 + 7a) 7(1(-5 + 7a) + 2a * (-5 + 7a)) = 0 7((-5 * 1 + 7a * 1) + 2a * (-5 + 7a)) = 0 7((-5 + 7a) + 2a * (-5 + 7a)) = 0 7(-5 + 7a + (-5 * 2a + 7a * 2a)) = 0 7(-5 + 7a + (-10a + 14a2)) = 0 Combine like terms: 7a + -10a = -3a 7(-5 + -3a + 14a2) = 0 (-5 * 7 + -3a * 7 + 14a2 * 7) = 0 (-35 + -21a + 98a2) = 0 Solving -35 + -21a + 98a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + -3a + 14a2) = 0 Factor a trinomial. 7((-1 + -2a)(5 + -7a)) = 0 Ignore the factor 7.Subproblem 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 '(5 + -7a)' equal to zero and attempt to solve: Simplifying 5 + -7a = 0 Solving 5 + -7a = 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 + -7a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7a = 0 + -5 -7a = 0 + -5 Combine like terms: 0 + -5 = -5 -7a = -5 Divide each side by '-7'. a = 0.7142857143 Simplifying a = 0.7142857143Solution
a = {-0.5, 0.7142857143}
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