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Simplifying 24a2 + -57ax + 18x2 = 0 Reorder the terms: -57ax + 24a2 + 18x2 = 0 Solving -57ax + 24a2 + 18x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19ax + 8a2 + 6x2) = 0 Factor a trinomial. 3((a + -2x)(8a + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(a + -2x)' equal to zero and attempt to solve: Simplifying a + -2x = 0 Solving a + -2x = 0 Move all terms containing a to the left, all other terms to the right. Add '2x' to each side of the equation. a + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 a + 0 = 0 + 2x a = 0 + 2x Remove the zero: a = 2x Simplifying a = 2xSubproblem 2
Set the factor '(8a + -3x)' equal to zero and attempt to solve: Simplifying 8a + -3x = 0 Solving 8a + -3x = 0 Move all terms containing a to the left, all other terms to the right. Add '3x' to each side of the equation. 8a + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 8a + 0 = 0 + 3x 8a = 0 + 3x Remove the zero: 8a = 3x Divide each side by '8'. a = 0.375x Simplifying a = 0.375xSolution
a = {2x, 0.375x}
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