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Simplifying 54a2 + -45ab + -54b2 = 0 Reorder the terms: -45ab + 54a2 + -54b2 = 0 Solving -45ab + 54a2 + -54b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9'. 9(-5ab + 6a2 + -6b2) = 0 Factor a trinomial. 9((2a + -3b)(3a + 2b)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {1.5b, -0.6666666667b}
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