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Simplifying 40a2 + -26ar + -30r2 = 0 Reorder the terms: -26ar + 40a2 + -30r2 = 0 Solving -26ar + 40a2 + -30r2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13ar + 20a2 + -15r2) = 0 Factor a trinomial. 2((4a + -5r)(5a + 3r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4a + -5r)' equal to zero and attempt to solve: Simplifying 4a + -5r = 0 Solving 4a + -5r = 0 Move all terms containing a to the left, all other terms to the right. Add '5r' to each side of the equation. 4a + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 4a + 0 = 0 + 5r 4a = 0 + 5r Remove the zero: 4a = 5r Divide each side by '4'. a = 1.25r Simplifying a = 1.25rSubproblem 2
Set the factor '(5a + 3r)' equal to zero and attempt to solve: Simplifying 5a + 3r = 0 Solving 5a + 3r = 0 Move all terms containing a to the left, all other terms to the right. Add '-3r' to each side of the equation. 5a + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 5a + 0 = 0 + -3r 5a = 0 + -3r Remove the zero: 5a = -3r Divide each side by '5'. a = -0.6r Simplifying a = -0.6rSolution
a = {1.25r, -0.6r}
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