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Simplifying 30r2 + 19ra + -63a2 = 0 Reorder the terms: 19ar + -63a2 + 30r2 = 0 Solving 19ar + -63a2 + 30r2 = 0 Solving for variable 'a'. Factor a trinomial. (-9a + -5r)(7a + -6r) = 0Subproblem 1
Set the factor '(-9a + -5r)' equal to zero and attempt to solve: Simplifying -9a + -5r = 0 Solving -9a + -5r = 0 Move all terms containing a to the left, all other terms to the right. Add '5r' to each side of the equation. -9a + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 -9a + 0 = 0 + 5r -9a = 0 + 5r Remove the zero: -9a = 5r Divide each side by '-9'. a = -0.5555555556r Simplifying a = -0.5555555556rSubproblem 2
Set the factor '(7a + -6r)' equal to zero and attempt to solve: Simplifying 7a + -6r = 0 Solving 7a + -6r = 0 Move all terms containing a to the left, all other terms to the right. Add '6r' to each side of the equation. 7a + -6r + 6r = 0 + 6r Combine like terms: -6r + 6r = 0 7a + 0 = 0 + 6r 7a = 0 + 6r Remove the zero: 7a = 6r Divide each side by '7'. a = 0.8571428571r Simplifying a = 0.8571428571rSolution
a = {-0.5555555556r, 0.8571428571r}
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