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Simplifying 42a2 + 19ad + -35d2 = 0 Reorder the terms: 19ad + 42a2 + -35d2 = 0 Solving 19ad + 42a2 + -35d2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -5d)(6a + 7d) = 0Subproblem 1
Set the factor '(7a + -5d)' equal to zero and attempt to solve: Simplifying 7a + -5d = 0 Solving 7a + -5d = 0 Move all terms containing a to the left, all other terms to the right. Add '5d' to each side of the equation. 7a + -5d + 5d = 0 + 5d Combine like terms: -5d + 5d = 0 7a + 0 = 0 + 5d 7a = 0 + 5d Remove the zero: 7a = 5d Divide each side by '7'. a = 0.7142857143d Simplifying a = 0.7142857143dSubproblem 2
Set the factor '(6a + 7d)' equal to zero and attempt to solve: Simplifying 6a + 7d = 0 Solving 6a + 7d = 0 Move all terms containing a to the left, all other terms to the right. Add '-7d' to each side of the equation. 6a + 7d + -7d = 0 + -7d Combine like terms: 7d + -7d = 0 6a + 0 = 0 + -7d 6a = 0 + -7d Remove the zero: 6a = -7d Divide each side by '6'. a = -1.166666667d Simplifying a = -1.166666667dSolution
a = {0.7142857143d, -1.166666667d}
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