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Simplifying 2a2 = -3a + 9 Reorder the terms: 2a2 = 9 + -3a Solving 2a2 = 9 + -3a Solving for variable 'a'. Reorder the terms: -9 + 3a + 2a2 = 9 + -3a + -9 + 3a Reorder the terms: -9 + 3a + 2a2 = 9 + -9 + -3a + 3a Combine like terms: 9 + -9 = 0 -9 + 3a + 2a2 = 0 + -3a + 3a -9 + 3a + 2a2 = -3a + 3a Combine like terms: -3a + 3a = 0 -9 + 3a + 2a2 = 0 Factor a trinomial. (-3 + -1a)(3 + -2a) = 0Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-3, 1.5}
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