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Simplifying (3a) = 1 + -3(3a) + -3a2 Remove parenthesis around (3a) (3a) = 1 + -3 * 3a + -3a2 Multiply -3 * 3 (3a) = 1 + -9a + -3a2 Solving (3a) = 1 + -9a + -3a2 Solving for variable 'a'. Reorder the terms: -1 + (3a) + 9a + 3a2 = 1 + -9a + -3a2 + -1 + 9a + 3a2 Combine like terms: (3a) + 9a = 12a -1 + 12a + 3a2 = 1 + -9a + -3a2 + -1 + 9a + 3a2 Reorder the terms: -1 + 12a + 3a2 = 1 + -1 + -9a + 9a + -3a2 + 3a2 Combine like terms: 1 + -1 = 0 -1 + 12a + 3a2 = 0 + -9a + 9a + -3a2 + 3a2 -1 + 12a + 3a2 = -9a + 9a + -3a2 + 3a2 Combine like terms: -9a + 9a = 0 -1 + 12a + 3a2 = 0 + -3a2 + 3a2 -1 + 12a + 3a2 = -3a2 + 3a2 Combine like terms: -3a2 + 3a2 = 0 -1 + 12a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 4a + a2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 4a + 0.3333333333 + a2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 4a + a2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 4a + a2 = 0 + 0.3333333333 4a + a2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 4a + a2 = 0.3333333333 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 0.3333333333 + 4 Reorder the terms: 4 + 4a + a2 = 0.3333333333 + 4 Combine like terms: 0.3333333333 + 4 = 4.3333333333 4 + 4a + a2 = 4.3333333333 Factor a perfect square on the left side: (a + 2)(a + 2) = 4.3333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (a + 2) equal to 2.081665999 and -2.081665999.Subproblem 1
a + 2 = 2.081665999 Simplifying a + 2 = 2.081665999 Reorder the terms: 2 + a = 2.081665999 Solving 2 + a = 2.081665999 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.081665999 + -2 a = 2.081665999 + -2 Combine like terms: 2.081665999 + -2 = 0.081665999 a = 0.081665999 Simplifying a = 0.081665999Subproblem 2
a + 2 = -2.081665999 Simplifying a + 2 = -2.081665999 Reorder the terms: 2 + a = -2.081665999 Solving 2 + a = -2.081665999 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.081665999 + -2 a = -2.081665999 + -2 Combine like terms: -2.081665999 + -2 = -4.081665999 a = -4.081665999 Simplifying a = -4.081665999Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.081665999, -4.081665999}
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