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Simplifying 50a3 + -18ab2 = 0 Reorder the terms: -18ab2 + 50a3 = 0 Solving -18ab2 + 50a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-9b2 + 25a2) = 0 Factor a difference between two squares. 2a((3b + 5a)(-3b + 5a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(3b + 5a)' equal to zero and attempt to solve: Simplifying 3b + 5a = 0 Reorder the terms: 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 = -0.6bSubproblem 3
Set the factor '(-3b + 5a)' equal to zero and attempt to solve: Simplifying -3b + 5a = 0 Reorder the terms: 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 = {0, -0.6b, 0.6b}
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