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Simplifying 2(a2 + 2) + -8 = -2a(a + -2) + -5 Reorder the terms: 2(2 + a2) + -8 = -2a(a + -2) + -5 (2 * 2 + a2 * 2) + -8 = -2a(a + -2) + -5 (4 + 2a2) + -8 = -2a(a + -2) + -5 Reorder the terms: 4 + -8 + 2a2 = -2a(a + -2) + -5 Combine like terms: 4 + -8 = -4 -4 + 2a2 = -2a(a + -2) + -5 Reorder the terms: -4 + 2a2 = -2a(-2 + a) + -5 -4 + 2a2 = (-2 * -2a + a * -2a) + -5 -4 + 2a2 = (4a + -2a2) + -5 Reorder the terms: -4 + 2a2 = -5 + 4a + -2a2 Solving -4 + 2a2 = -5 + 4a + -2a2 Solving for variable 'a'. Reorder the terms: -4 + 5 + -4a + 2a2 + 2a2 = -5 + 4a + -2a2 + 5 + -4a + 2a2 Combine like terms: -4 + 5 = 1 1 + -4a + 2a2 + 2a2 = -5 + 4a + -2a2 + 5 + -4a + 2a2 Combine like terms: 2a2 + 2a2 = 4a2 1 + -4a + 4a2 = -5 + 4a + -2a2 + 5 + -4a + 2a2 Reorder the terms: 1 + -4a + 4a2 = -5 + 5 + 4a + -4a + -2a2 + 2a2 Combine like terms: -5 + 5 = 0 1 + -4a + 4a2 = 0 + 4a + -4a + -2a2 + 2a2 1 + -4a + 4a2 = 4a + -4a + -2a2 + 2a2 Combine like terms: 4a + -4a = 0 1 + -4a + 4a2 = 0 + -2a2 + 2a2 1 + -4a + 4a2 = -2a2 + 2a2 Combine like terms: -2a2 + 2a2 = 0 1 + -4a + 4a2 = 0 Factor a trinomial. (1 + -2a)(1 + -2a) = 0Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {0.5, 0.5}
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