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Simplifying 2a2 + 3a + -7 = 20 Reorder the terms: -7 + 3a + 2a2 = 20 Solving -7 + 3a + 2a2 = 20 Solving for variable 'a'. Reorder the terms: -7 + -20 + 3a + 2a2 = 20 + -20 Combine like terms: -7 + -20 = -27 -27 + 3a + 2a2 = 20 + -20 Combine like terms: 20 + -20 = 0 -27 + 3a + 2a2 = 0 Factor a trinomial. (-9 + -2a)(3 + -1a) = 0Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve: Simplifying -9 + -2a = 0 Solving -9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2a = 0 + 9 -2a = 0 + 9 Combine like terms: 0 + 9 = 9 -2a = 9 Divide each side by '-2'. a = -4.5 Simplifying a = -4.5Subproblem 2
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 = 3Solution
a = {-4.5, 3}
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