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Simplifying 0 = 4a2 + 8a + -21 Reorder the terms: 0 = -21 + 8a + 4a2 Solving 0 = -21 + 8a + 4a2 Solving for variable 'a'. Combine like terms: 0 + 21 = 21 21 + -8a + -4a2 = -21 + 8a + 4a2 + 21 + -8a + -4a2 Reorder the terms: 21 + -8a + -4a2 = -21 + 21 + 8a + -8a + 4a2 + -4a2 Combine like terms: -21 + 21 = 0 21 + -8a + -4a2 = 0 + 8a + -8a + 4a2 + -4a2 21 + -8a + -4a2 = 8a + -8a + 4a2 + -4a2 Combine like terms: 8a + -8a = 0 21 + -8a + -4a2 = 0 + 4a2 + -4a2 21 + -8a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 21 + -8a + -4a2 = 0 Factor a trinomial. (3 + -2a)(7 + 2a) = 0Subproblem 1
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Subproblem 2
Set the factor '(7 + 2a)' equal to zero and attempt to solve: Simplifying 7 + 2a = 0 Solving 7 + 2a = 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 + 2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2a = 0 + -7 2a = 0 + -7 Combine like terms: 0 + -7 = -7 2a = -7 Divide each side by '2'. a = -3.5 Simplifying a = -3.5Solution
a = {1.5, -3.5}
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