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Simplifying 27a2 + -21aq + 36aq + -28q2 = 0 Reorder the terms: -21aq + 36aq + 27a2 + -28q2 = 0 Combine like terms: -21aq + 36aq = 15aq 15aq + 27a2 + -28q2 = 0 Solving 15aq + 27a2 + -28q2 = 0 Solving for variable 'a'. Factor a trinomial. (9a + -7q)(3a + 4q) = 0Subproblem 1
Set the factor '(9a + -7q)' equal to zero and attempt to solve: Simplifying 9a + -7q = 0 Solving 9a + -7q = 0 Move all terms containing a to the left, all other terms to the right. Add '7q' to each side of the equation. 9a + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 9a + 0 = 0 + 7q 9a = 0 + 7q Remove the zero: 9a = 7q Divide each side by '9'. a = 0.7777777778q Simplifying a = 0.7777777778qSubproblem 2
Set the factor '(3a + 4q)' equal to zero and attempt to solve: Simplifying 3a + 4q = 0 Solving 3a + 4q = 0 Move all terms containing a to the left, all other terms to the right. Add '-4q' to each side of the equation. 3a + 4q + -4q = 0 + -4q Combine like terms: 4q + -4q = 0 3a + 0 = 0 + -4q 3a = 0 + -4q Remove the zero: 3a = -4q Divide each side by '3'. a = -1.333333333q Simplifying a = -1.333333333qSolution
a = {0.7777777778q, -1.333333333q}
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