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Simplifying 2x2 + -7ax + 4a2 = a2 Reorder the terms: -7ax + 4a2 + 2x2 = a2 Solving -7ax + 4a2 + 2x2 = a2 Solving for variable 'a'. Reorder the terms: -7ax + 4a2 + -1a2 + 2x2 = a2 + -1a2 Combine like terms: 4a2 + -1a2 = 3a2 -7ax + 3a2 + 2x2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -7ax + 3a2 + 2x2 = 0 Factor a trinomial. (a + -2x)(3a + -1x) = 0Subproblem 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 '(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 = 0.3333333333xSolution
a = {2x, 0.3333333333x}
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