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Simplifying 27a2 + 39ad + 14d2 = 0 Reorder the terms: 39ad + 27a2 + 14d2 = 0 Solving 39ad + 27a2 + 14d2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + 2d)(9a + 7d) = 0Subproblem 1
Set the factor '(3a + 2d)' equal to zero and attempt to solve: Simplifying 3a + 2d = 0 Solving 3a + 2d = 0 Move all terms containing a to the left, all other terms to the right. Add '-2d' to each side of the equation. 3a + 2d + -2d = 0 + -2d Combine like terms: 2d + -2d = 0 3a + 0 = 0 + -2d 3a = 0 + -2d Remove the zero: 3a = -2d Divide each side by '3'. a = -0.6666666667d Simplifying a = -0.6666666667dSubproblem 2
Set the factor '(9a + 7d)' equal to zero and attempt to solve: Simplifying 9a + 7d = 0 Solving 9a + 7d = 0 Move all terms containing a to the left, all other terms to the right. Add '-7d' to each side of the equation. 9a + 7d + -7d = 0 + -7d Combine like terms: 7d + -7d = 0 9a + 0 = 0 + -7d 9a = 0 + -7d Remove the zero: 9a = -7d Divide each side by '9'. a = -0.7777777778d Simplifying a = -0.7777777778dSolution
a = {-0.6666666667d, -0.7777777778d}
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