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Simplifying x2 + -2ax = 8a2 Reorder the terms: -2ax + x2 = 8a2 Solving -2ax + x2 = 8a2 Solving for variable 'a'. Reorder the terms: -2ax + -8a2 + x2 = 8a2 + -8a2 Combine like terms: 8a2 + -8a2 = 0 -2ax + -8a2 + x2 = 0 Factor a trinomial. (-2a + -1x)(4a + -1x) = 0Subproblem 1
Set the factor '(-2a + -1x)' equal to zero and attempt to solve: Simplifying -2a + -1x = 0 Solving -2a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -2a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -2a + 0 = 0 + x -2a = 0 + x Remove the zero: -2a = x Divide each side by '-2'. a = -0.5x Simplifying a = -0.5xSubproblem 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 = {-0.5x, 0.25x}
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