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Simplifying 9a4 + 11a3b + 2a2b2 = 0 Reorder the terms: 2a2b2 + 11a3b + 9a4 = 0 Solving 2a2b2 + 11a3b + 9a4 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a2'. a2(2b2 + 11ab + 9a2) = 0 Factor a trinomial. a2((b + a)(2b + 9a)) = 0Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(b + a)' equal to zero and attempt to solve: Simplifying b + a = 0 Reorder the terms: a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 3
Set the factor '(2b + 9a)' equal to zero and attempt to solve: Simplifying 2b + 9a = 0 Reorder the terms: 9a + 2b = 0 Solving 9a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 9a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 9a + 0 = 0 + -2b 9a = 0 + -2b Remove the zero: 9a = -2b Divide each side by '9'. a = -0.2222222222b Simplifying a = -0.2222222222bSolution
a = {0, -1b, -0.2222222222b}
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