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Simplifying 378a2 + -147a + -343 = 0 Reorder the terms: -343 + -147a + 378a2 = 0 Solving -343 + -147a + 378a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(-49 + -21a + 54a2) = 0 Factor a trinomial. 7((-7 + -9a)(7 + -6a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-7 + -9a)' equal to zero and attempt to solve: Simplifying -7 + -9a = 0 Solving -7 + -9a = 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 + -9a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9a = 0 + 7 -9a = 0 + 7 Combine like terms: 0 + 7 = 7 -9a = 7 Divide each side by '-9'. a = -0.7777777778 Simplifying a = -0.7777777778Subproblem 2
Set the factor '(7 + -6a)' equal to zero and attempt to solve: Simplifying 7 + -6a = 0 Solving 7 + -6a = 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 + -6a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6a = 0 + -7 -6a = 0 + -7 Combine like terms: 0 + -7 = -7 -6a = -7 Divide each side by '-6'. a = 1.166666667 Simplifying a = 1.166666667Solution
a = {-0.7777777778, 1.166666667}
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