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Simplifying 10a2 + -41ab + 21b2 = 0 Reorder the terms: -41ab + 10a2 + 21b2 = 0 Solving -41ab + 10a2 + 21b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -7b)(5a + -3b) = 0Subproblem 1
Set the factor '(2a + -7b)' equal to zero and attempt to solve: Simplifying 2a + -7b = 0 Solving 2a + -7b = 0 Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 2a + -7b + 7b = 0 + 7b Combine like terms: -7b + 7b = 0 2a + 0 = 0 + 7b 2a = 0 + 7b Remove the zero: 2a = 7b Divide each side by '2'. a = 3.5b Simplifying a = 3.5bSubproblem 2
Set the factor '(5a + -3b)' equal to zero and attempt to solve: Simplifying 5a + -3b = 0 Solving 5a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 5a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 5a + 0 = 0 + 3b 5a = 0 + 3b Remove the zero: 5a = 3b Divide each side by '5'. a = 0.6b Simplifying a = 0.6bSolution
a = {3.5b, 0.6b}
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