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Simplifying 12v2 + 13va + -35a2 = 0 Reorder the terms: 13av + -35a2 + 12v2 = 0 Solving 13av + -35a2 + 12v2 = 0 Solving for variable 'a'. Factor a trinomial. (-7a + -3v)(5a + -4v) = 0Subproblem 1
Set the factor '(-7a + -3v)' equal to zero and attempt to solve: Simplifying -7a + -3v = 0 Solving -7a + -3v = 0 Move all terms containing a to the left, all other terms to the right. Add '3v' to each side of the equation. -7a + -3v + 3v = 0 + 3v Combine like terms: -3v + 3v = 0 -7a + 0 = 0 + 3v -7a = 0 + 3v Remove the zero: -7a = 3v Divide each side by '-7'. a = -0.4285714286v Simplifying a = -0.4285714286vSubproblem 2
Set the factor '(5a + -4v)' equal to zero and attempt to solve: Simplifying 5a + -4v = 0 Solving 5a + -4v = 0 Move all terms containing a to the left, all other terms to the right. Add '4v' to each side of the equation. 5a + -4v + 4v = 0 + 4v Combine like terms: -4v + 4v = 0 5a + 0 = 0 + 4v 5a = 0 + 4v Remove the zero: 5a = 4v Divide each side by '5'. a = 0.8v Simplifying a = 0.8vSolution
a = {-0.4285714286v, 0.8v}
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