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Simplifying 14a2 + 5ab + -6b2 = 0 Reorder the terms: 5ab + 14a2 + -6b2 = 0 Solving 5ab + 14a2 + -6b2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -1b)(7a + 6b) = 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 '(7a + 6b)' equal to zero and attempt to solve: Simplifying 7a + 6b = 0 Solving 7a + 6b = 0 Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 7a + 6b + -6b = 0 + -6b Combine like terms: 6b + -6b = 0 7a + 0 = 0 + -6b 7a = 0 + -6b Remove the zero: 7a = -6b Divide each side by '7'. a = -0.8571428571b Simplifying a = -0.8571428571bSolution
a = {0.5b, -0.8571428571b}
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