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Simplifying x2 + xa + -42a2 = 0 Reorder the terms: ax + -42a2 + x2 = 0 Solving ax + -42a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (-7a + -1x)(6a + -1x) = 0Subproblem 1
Set the factor '(-7a + -1x)' equal to zero and attempt to solve: Simplifying -7a + -1x = 0 Solving -7a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -7a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -7a + 0 = 0 + x -7a = 0 + x Remove the zero: -7a = x Divide each side by '-7'. a = -0.1428571429x Simplifying a = -0.1428571429xSubproblem 2
Set the factor '(6a + -1x)' equal to zero and attempt to solve: Simplifying 6a + -1x = 0 Solving 6a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. 6a + -1x + x = 0 + x Combine like terms: -1x + x = 0 6a + 0 = 0 + x 6a = 0 + x Remove the zero: 6a = x Divide each side by '6'. a = 0.1666666667x Simplifying a = 0.1666666667xSolution
a = {-0.1428571429x, 0.1666666667x}
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