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Simplifying 3a2 = 5a + 22 Reorder the terms: 3a2 = 22 + 5a Solving 3a2 = 22 + 5a Solving for variable 'a'. Reorder the terms: -22 + -5a + 3a2 = 22 + 5a + -22 + -5a Reorder the terms: -22 + -5a + 3a2 = 22 + -22 + 5a + -5a Combine like terms: 22 + -22 = 0 -22 + -5a + 3a2 = 0 + 5a + -5a -22 + -5a + 3a2 = 5a + -5a Combine like terms: 5a + -5a = 0 -22 + -5a + 3a2 = 0 Factor a trinomial. (-2 + -1a)(11 + -3a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(11 + -3a)' equal to zero and attempt to solve: Simplifying 11 + -3a = 0 Solving 11 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3a = 0 + -11 -3a = 0 + -11 Combine like terms: 0 + -11 = -11 -3a = -11 Divide each side by '-3'. a = 3.666666667 Simplifying a = 3.666666667Solution
a = {-2, 3.666666667}
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