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Simplifying 4a + -1(a + -2) = 2a(3a + -2) Reorder the terms: 4a + -1(-2 + a) = 2a(3a + -2) 4a + (-2 * -1 + a * -1) = 2a(3a + -2) 4a + (2 + -1a) = 2a(3a + -2) Reorder the terms: 2 + 4a + -1a = 2a(3a + -2) Combine like terms: 4a + -1a = 3a 2 + 3a = 2a(3a + -2) Reorder the terms: 2 + 3a = 2a(-2 + 3a) 2 + 3a = (-2 * 2a + 3a * 2a) 2 + 3a = (-4a + 6a2) Solving 2 + 3a = -4a + 6a2 Solving for variable 'a'. Combine like terms: 3a + 4a = 7a 2 + 7a + -6a2 = -4a + 6a2 + 4a + -6a2 Reorder the terms: 2 + 7a + -6a2 = -4a + 4a + 6a2 + -6a2 Combine like terms: -4a + 4a = 0 2 + 7a + -6a2 = 0 + 6a2 + -6a2 2 + 7a + -6a2 = 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 2 + 7a + -6a2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.3333333333 + -1.166666667a + a2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.166666667a + 0.3333333333 + a2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.166666667a + a2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.166666667a + a2 = 0 + 0.3333333333 -1.166666667a + a2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.166666667a + a2 = 0.3333333333 The a term is -1.166666667a. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667a + 0.3402777780 + a2 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667a + a2 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + -1.166666667a + a2 = 0.6736111113 Factor a perfect square on the left side: (a + -0.5833333335)(a + -0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (a + -0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
a + -0.5833333335 = 0.82073815 Simplifying a + -0.5833333335 = 0.82073815 Reorder the terms: -0.5833333335 + a = 0.82073815 Solving -0.5833333335 + a = 0.82073815 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = 0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = 0.82073815 + 0.5833333335 a = 0.82073815 + 0.5833333335 Combine like terms: 0.82073815 + 0.5833333335 = 1.4040714835 a = 1.4040714835 Simplifying a = 1.4040714835Subproblem 2
a + -0.5833333335 = -0.82073815 Simplifying a + -0.5833333335 = -0.82073815 Reorder the terms: -0.5833333335 + a = -0.82073815 Solving -0.5833333335 + a = -0.82073815 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = -0.82073815 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = -0.82073815 + 0.5833333335 a = -0.82073815 + 0.5833333335 Combine like terms: -0.82073815 + 0.5833333335 = -0.2374048165 a = -0.2374048165 Simplifying a = -0.2374048165Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.4040714835, -0.2374048165}
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