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Simplifying -8a2 + 2ab + 3b2 = 0 Reorder the terms: 2ab + -8a2 + 3b2 = 0 Solving 2ab + -8a2 + 3b2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -1b)(4a + -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 '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSolution
a = {-0.5b, 0.75b}
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