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Simplifying 8a2 + 30a + -27 = 0 Reorder the terms: -27 + 30a + 8a2 = 0 Solving -27 + 30a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -2a)(3 + -4a) = 0Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve: Simplifying -9 + -2a = 0 Solving -9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2a = 0 + 9 -2a = 0 + 9 Combine like terms: 0 + 9 = 9 -2a = 9 Divide each side by '-2'. a = -4.5 Simplifying a = -4.5Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {-4.5, 0.75}
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