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Simplifying 5x2 + -5ax + -60a2 = 0 Reorder the terms: -5ax + -60a2 + 5x2 = 0 Solving -5ax + -60a2 + 5x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1ax + -12a2 + x2) = 0 Factor a trinomial. 5((-3a + -1x)(4a + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3a + -1x)' equal to zero and attempt to solve: Simplifying -3a + -1x = 0 Solving -3a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -3a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -3a + 0 = 0 + x -3a = 0 + x Remove the zero: -3a = x Divide each side by '-3'. a = -0.3333333333x Simplifying a = -0.3333333333xSubproblem 2
Set the factor '(4a + -1x)' equal to zero and attempt to solve: Simplifying 4a + -1x = 0 Solving 4a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. 4a + -1x + x = 0 + x Combine like terms: -1x + x = 0 4a + 0 = 0 + x 4a = 0 + x Remove the zero: 4a = x Divide each side by '4'. a = 0.25x Simplifying a = 0.25xSolution
a = {-0.3333333333x, 0.25x}
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