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Simplifying ((5a + 2) + (5a2 + -6)) + -1(3a2 + -4a + 7) = 0 Reorder the terms: ((2 + 5a) + (5a2 + -6)) + -1(3a2 + -4a + 7) = 0 Remove parenthesis around (2 + 5a) (2 + 5a + (5a2 + -6)) + -1(3a2 + -4a + 7) = 0 Reorder the terms: (2 + 5a + (-6 + 5a2)) + -1(3a2 + -4a + 7) = 0 Remove parenthesis around (-6 + 5a2) (2 + 5a + -6 + 5a2) + -1(3a2 + -4a + 7) = 0 Reorder the terms: (2 + -6 + 5a + 5a2) + -1(3a2 + -4a + 7) = 0 Combine like terms: 2 + -6 = -4 (-4 + 5a + 5a2) + -1(3a2 + -4a + 7) = 0 Remove parenthesis around (-4 + 5a + 5a2) -4 + 5a + 5a2 + -1(3a2 + -4a + 7) = 0 Reorder the terms: -4 + 5a + 5a2 + -1(7 + -4a + 3a2) = 0 -4 + 5a + 5a2 + (7 * -1 + -4a * -1 + 3a2 * -1) = 0 -4 + 5a + 5a2 + (-7 + 4a + -3a2) = 0 Reorder the terms: -4 + -7 + 5a + 4a + 5a2 + -3a2 = 0 Combine like terms: -4 + -7 = -11 -11 + 5a + 4a + 5a2 + -3a2 = 0 Combine like terms: 5a + 4a = 9a -11 + 9a + 5a2 + -3a2 = 0 Combine like terms: 5a2 + -3a2 = 2a2 -11 + 9a + 2a2 = 0 Solving -11 + 9a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-11 + -2a)(1 + -1a) = 0Subproblem 1
Set the factor '(-11 + -2a)' equal to zero and attempt to solve: Simplifying -11 + -2a = 0 Solving -11 + -2a = 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 + -2a = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2a = 0 + 11 -2a = 0 + 11 Combine like terms: 0 + 11 = 11 -2a = 11 Divide each side by '-2'. a = -5.5 Simplifying a = -5.5Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-5.5, 1}
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