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Simplifying 32a2 + -48ab + 18b2 = 0 Reorder the terms: -48ab + 32a2 + 18b2 = 0 Solving -48ab + 32a2 + 18b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24ab + 16a2 + 9b2) = 0 Factor a trinomial. 2((4a + -3b)(4a + -3b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSubproblem 2
Set the factor '(4a + -3b)' equal to zero and attempt to solve: Simplifying 4a + -3b = 0 Solving 4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 4a + 0 = 0 + 3b 4a = 0 + 3b Remove the zero: 4a = 3b Divide each side by '4'. a = 0.75b Simplifying a = 0.75bSolution
a = {0.75b, 0.75b}
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