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Simplifying 56a2 + 19ar + -15r2 = 0 Reorder the terms: 19ar + 56a2 + -15r2 = 0 Solving 19ar + 56a2 + -15r2 = 0 Solving for variable 'a'. Factor a trinomial. (8a + -3r)(7a + 5r) = 0Subproblem 1
Set the factor '(8a + -3r)' equal to zero and attempt to solve: Simplifying 8a + -3r = 0 Solving 8a + -3r = 0 Move all terms containing a to the left, all other terms to the right. Add '3r' to each side of the equation. 8a + -3r + 3r = 0 + 3r Combine like terms: -3r + 3r = 0 8a + 0 = 0 + 3r 8a = 0 + 3r Remove the zero: 8a = 3r Divide each side by '8'. a = 0.375r Simplifying a = 0.375rSubproblem 2
Set the factor '(7a + 5r)' equal to zero and attempt to solve: Simplifying 7a + 5r = 0 Solving 7a + 5r = 0 Move all terms containing a to the left, all other terms to the right. Add '-5r' to each side of the equation. 7a + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 7a + 0 = 0 + -5r 7a = 0 + -5r Remove the zero: 7a = -5r Divide each side by '7'. a = -0.7142857143r Simplifying a = -0.7142857143rSolution
a = {0.375r, -0.7142857143r}
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