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Simplifying 10a2 + 31ab + -14b2 = 0 Reorder the terms: 31ab + 10a2 + -14b2 = 0 Solving 31ab + 10a2 + -14b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -2b)(2a + 7b) = 0Subproblem 1
Set the factor '(5a + -2b)' equal to zero and attempt to solve: Simplifying 5a + -2b = 0 Solving 5a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 5a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 5a + 0 = 0 + 2b 5a = 0 + 2b Remove the zero: 5a = 2b Divide each side by '5'. a = 0.4b Simplifying a = 0.4bSubproblem 2
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 = -3.5bSolution
a = {0.4b, -3.5b}
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