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Simplifying x2 + -7ax + 12a2 = 0 Reorder the terms: -7ax + 12a2 + x2 = 0 Solving -7ax + 12a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -1x)(4a + -1x) = 0Subproblem 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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