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Simplifying 3b2 + 5ab + -2a2 = 0 Reorder the terms: 5ab + -2a2 + 3b2 = 0 Solving 5ab + -2a2 + 3b2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -1b)(a + -3b) = 0Subproblem 1
Set the factor '(-2a + -1b)' equal to zero and attempt to solve: Simplifying -2a + -1b = 0 Solving -2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. -2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 -2a + 0 = 0 + b -2a = 0 + b Remove the zero: -2a = b Divide each side by '-2'. a = -0.5b Simplifying a = -0.5bSubproblem 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 = {-0.5b, 3b}
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