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Simplifying x2 + 4ax = 21a2 Reorder the terms: 4ax + x2 = 21a2 Solving 4ax + x2 = 21a2 Solving for variable 'a'. Reorder the terms: 4ax + -21a2 + x2 = 21a2 + -21a2 Combine like terms: 21a2 + -21a2 = 0 4ax + -21a2 + x2 = 0 Factor a trinomial. (-7a + -1x)(3a + -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 '(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 = {-0.1428571429x, 0.3333333333x}
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