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Simplifying a2 + 8ad + 15d2 = 0 Reorder the terms: 8ad + a2 + 15d2 = 0 Solving 8ad + a2 + 15d2 = 0 Solving for variable 'a'. Factor a trinomial. (a + 3d)(a + 5d) = 0Subproblem 1
Set the factor '(a + 3d)' equal to zero and attempt to solve: Simplifying a + 3d = 0 Solving a + 3d = 0 Move all terms containing a to the left, all other terms to the right. Add '-3d' to each side of the equation. a + 3d + -3d = 0 + -3d Combine like terms: 3d + -3d = 0 a + 0 = 0 + -3d a = 0 + -3d Remove the zero: a = -3d Simplifying a = -3dSubproblem 2
Set the factor '(a + 5d)' equal to zero and attempt to solve: Simplifying a + 5d = 0 Solving a + 5d = 0 Move all terms containing a to the left, all other terms to the right. Add '-5d' to each side of the equation. a + 5d + -5d = 0 + -5d Combine like terms: 5d + -5d = 0 a + 0 = 0 + -5d a = 0 + -5d Remove the zero: a = -5d Simplifying a = -5dSolution
a = {-3d, -5d}
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