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Simplifying 20a2 + 17ar + -63r2 = 0 Reorder the terms: 17ar + 20a2 + -63r2 = 0 Solving 17ar + 20a2 + -63r2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -7r)(4a + 9r) = 0Subproblem 1
Set the factor '(5a + -7r)' equal to zero and attempt to solve: Simplifying 5a + -7r = 0 Solving 5a + -7r = 0 Move all terms containing a to the left, all other terms to the right. Add '7r' to each side of the equation. 5a + -7r + 7r = 0 + 7r Combine like terms: -7r + 7r = 0 5a + 0 = 0 + 7r 5a = 0 + 7r Remove the zero: 5a = 7r Divide each side by '5'. a = 1.4r Simplifying a = 1.4rSubproblem 2
Set the factor '(4a + 9r)' equal to zero and attempt to solve: Simplifying 4a + 9r = 0 Solving 4a + 9r = 0 Move all terms containing a to the left, all other terms to the right. Add '-9r' to each side of the equation. 4a + 9r + -9r = 0 + -9r Combine like terms: 9r + -9r = 0 4a + 0 = 0 + -9r 4a = 0 + -9r Remove the zero: 4a = -9r Divide each side by '4'. a = -2.25r Simplifying a = -2.25rSolution
a = {1.4r, -2.25r}
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