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Simplifying -1x2 + 3ax = 2a2 Reorder the terms: 3ax + -1x2 = 2a2 Solving 3ax + -1x2 = 2a2 Solving for variable 'a'. Reorder the terms: 3ax + -2a2 + -1x2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 3ax + -2a2 + -1x2 = 0 Factor a trinomial. (-2a + x)(a + -1x) = 0Subproblem 1
Set the factor '(-2a + x)' equal to zero and attempt to solve: Simplifying -2a + x = 0 Solving -2a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. -2a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -2a + 0 = 0 + -1x -2a = 0 + -1x Remove the zero: -2a = -1x Divide each side by '-2'. a = 0.5x Simplifying a = 0.5xSubproblem 2
Set the factor '(a + -1x)' equal to zero and attempt to solve: Simplifying a + -1x = 0 Solving a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. a + -1x + x = 0 + x Combine like terms: -1x + x = 0 a + 0 = 0 + x a = 0 + x Remove the zero: a = x Simplifying a = xSolution
a = {0.5x, x}
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