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Simplifying 5a2 + 8ab + -21b2 = 0 Reorder the terms: 8ab + 5a2 + -21b2 = 0 Solving 8ab + 5a2 + -21b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -7b)(a + 3b) = 0Subproblem 1
Set the factor '(5a + -7b)' equal to zero and attempt to solve: Simplifying 5a + -7b = 0 Solving 5a + -7b = 0 Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 5a + -7b + 7b = 0 + 7b Combine like terms: -7b + 7b = 0 5a + 0 = 0 + 7b 5a = 0 + 7b Remove the zero: 5a = 7b Divide each side by '5'. a = 1.4b Simplifying a = 1.4bSubproblem 2
Set the factor '(a + 3b)' equal to zero and attempt to solve: Simplifying a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3bSolution
a = {1.4b, -3b}
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