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Simplifying x2 + 12ax + 35a2 = 0 Reorder the terms: 12ax + 35a2 + x2 = 0 Solving 12ax + 35a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + x)(5a + x) = 0Subproblem 1
Set the factor '(7a + x)' equal to zero and attempt to solve: Simplifying 7a + x = 0 Solving 7a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 7a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 7a + 0 = 0 + -1x 7a = 0 + -1x Remove the zero: 7a = -1x Divide each side by '7'. a = -0.1428571429x Simplifying a = -0.1428571429xSubproblem 2
Set the factor '(5a + x)' equal to zero and attempt to solve: Simplifying 5a + x = 0 Solving 5a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 5a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 5a + 0 = 0 + -1x 5a = 0 + -1x Remove the zero: 5a = -1x Divide each side by '5'. a = -0.2x Simplifying a = -0.2xSolution
a = {-0.1428571429x, -0.2x}
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