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Simplifying 75a2 + -30ab + 3b2 = 0 Reorder the terms: -30ab + 75a2 + 3b2 = 0 Solving -30ab + 75a2 + 3b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10ab + 25a2 + b2) = 0 Factor a trinomial. 3((5a + -1b)(5a + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2bSubproblem 2
Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2bSolution
a = {0.2b, 0.2b}
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