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Simplifying 12a2 + 13ad + -35d2 = 0 Reorder the terms: 13ad + 12a2 + -35d2 = 0 Solving 13ad + 12a2 + -35d2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -5d)(3a + 7d) = 0Subproblem 1
Set the factor '(4a + -5d)' equal to zero and attempt to solve: Simplifying 4a + -5d = 0 Solving 4a + -5d = 0 Move all terms containing a to the left, all other terms to the right. Add '5d' to each side of the equation. 4a + -5d + 5d = 0 + 5d Combine like terms: -5d + 5d = 0 4a + 0 = 0 + 5d 4a = 0 + 5d Remove the zero: 4a = 5d Divide each side by '4'. a = 1.25d Simplifying a = 1.25dSubproblem 2
Set the factor '(3a + 7d)' equal to zero and attempt to solve: Simplifying 3a + 7d = 0 Solving 3a + 7d = 0 Move all terms containing a to the left, all other terms to the right. Add '-7d' to each side of the equation. 3a + 7d + -7d = 0 + -7d Combine like terms: 7d + -7d = 0 3a + 0 = 0 + -7d 3a = 0 + -7d Remove the zero: 3a = -7d Divide each side by '3'. a = -2.333333333d Simplifying a = -2.333333333dSolution
a = {1.25d, -2.333333333d}
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