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Simplifying 6a2 + 37a + -42 = -7 Reorder the terms: -42 + 37a + 6a2 = -7 Solving -42 + 37a + 6a2 = -7 Solving for variable 'a'. Reorder the terms: -42 + 7 + 37a + 6a2 = -7 + 7 Combine like terms: -42 + 7 = -35 -35 + 37a + 6a2 = -7 + 7 Combine like terms: -7 + 7 = 0 -35 + 37a + 6a2 = 0 Factor a trinomial. (-7 + -1a)(5 + -6a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 2
Set the factor '(5 + -6a)' equal to zero and attempt to solve: Simplifying 5 + -6a = 0 Solving 5 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6a = 0 + -5 -6a = 0 + -5 Combine like terms: 0 + -5 = -5 -6a = -5 Divide each side by '-6'. a = 0.8333333333 Simplifying a = 0.8333333333Solution
a = {-7, 0.8333333333}
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