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Simplifying 21a2 + 32ab + -5b2 = 0 Reorder the terms: 32ab + 21a2 + -5b2 = 0 Solving 32ab + 21a2 + -5b2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -1b)(3a + 5b) = 0Subproblem 1
Set the factor '(7a + -1b)' equal to zero and attempt to solve: Simplifying 7a + -1b = 0 Solving 7a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 7a + -1b + b = 0 + b Combine like terms: -1b + b = 0 7a + 0 = 0 + b 7a = 0 + b Remove the zero: 7a = b Divide each side by '7'. a = 0.1428571429b Simplifying a = 0.1428571429bSubproblem 2
Set the factor '(3a + 5b)' equal to zero and attempt to solve: Simplifying 3a + 5b = 0 Solving 3a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 3a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 3a + 0 = 0 + -5b 3a = 0 + -5b Remove the zero: 3a = -5b Divide each side by '3'. a = -1.666666667b Simplifying a = -1.666666667bSolution
a = {0.1428571429b, -1.666666667b}
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