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Simplifying 10a2 + -23ab + -5b2 = 0 Reorder the terms: -23ab + 10a2 + -5b2 = 0 Solving -23ab + 10a2 + -5b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -5b)(5a + b) = 0Subproblem 1
Set the factor '(2a + -5b)' equal to zero and attempt to solve: Simplifying 2a + -5b = 0 Solving 2a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 2a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 2a + 0 = 0 + 5b 2a = 0 + 5b Remove the zero: 2a = 5b Divide each side by '2'. a = 2.5b Simplifying a = 2.5bSubproblem 2
Set the factor '(5a + b)' equal to zero and attempt to solve: Simplifying 5a + b = 0 Solving 5a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 5a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 5a + 0 = 0 + -1b 5a = 0 + -1b Remove the zero: 5a = -1b Divide each side by '5'. a = -0.2b Simplifying a = -0.2bSolution
a = {2.5b, -0.2b}
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