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Simplifying (2a2 + 5a + -3) + -1(5a2 + 4a + -7) = 0 Reorder the terms: (-3 + 5a + 2a2) + -1(5a2 + 4a + -7) = 0 Remove parenthesis around (-3 + 5a + 2a2) -3 + 5a + 2a2 + -1(5a2 + 4a + -7) = 0 Reorder the terms: -3 + 5a + 2a2 + -1(-7 + 4a + 5a2) = 0 -3 + 5a + 2a2 + (-7 * -1 + 4a * -1 + 5a2 * -1) = 0 -3 + 5a + 2a2 + (7 + -4a + -5a2) = 0 Reorder the terms: -3 + 7 + 5a + -4a + 2a2 + -5a2 = 0 Combine like terms: -3 + 7 = 4 4 + 5a + -4a + 2a2 + -5a2 = 0 Combine like terms: 5a + -4a = 1a 4 + 1a + 2a2 + -5a2 = 0 Combine like terms: 2a2 + -5a2 = -3a2 4 + 1a + -3a2 = 0 Solving 4 + 1a + -3a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + -3a)(1 + a) = 0Subproblem 1
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {1.333333333, -1}
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