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Simplifying 4a2 + -19a + 19 = -2 Reorder the terms: 19 + -19a + 4a2 = -2 Solving 19 + -19a + 4a2 = -2 Solving for variable 'a'. Reorder the terms: 19 + 2 + -19a + 4a2 = -2 + 2 Combine like terms: 19 + 2 = 21 21 + -19a + 4a2 = -2 + 2 Combine like terms: -2 + 2 = 0 21 + -19a + 4a2 = 0 Factor a trinomial. (7 + -4a)(3 + -1a) = 0Subproblem 1
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 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 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Subproblem 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 = {1.75, 3}
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