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Simplifying 14a2 = 210 + -49a Solving 14a2 = 210 + -49a Solving for variable 'a'. Reorder the terms: -210 + 49a + 14a2 = 210 + -49a + -210 + 49a Reorder the terms: -210 + 49a + 14a2 = 210 + -210 + -49a + 49a Combine like terms: 210 + -210 = 0 -210 + 49a + 14a2 = 0 + -49a + 49a -210 + 49a + 14a2 = -49a + 49a Combine like terms: -49a + 49a = 0 -210 + 49a + 14a2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-30 + 7a + 2a2) = 0 Factor a trinomial. 7((-6 + -1a)(5 + -2a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6Subproblem 2
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 = 2.5Solution
a = {-6, 2.5}
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