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Simplifying 144a2 + -168a = 49 Reorder the terms: -168a + 144a2 = 49 Solving -168a + 144a2 = 49 Solving for variable 'a'. Reorder the terms: -49 + -168a + 144a2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -168a + 144a2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.3402777778 + -1.166666667a + a2 = 0 Move the constant term to the right: Add '0.3402777778' to each side of the equation. -0.3402777778 + -1.166666667a + 0.3402777778 + a2 = 0 + 0.3402777778 Reorder the terms: -0.3402777778 + 0.3402777778 + -1.166666667a + a2 = 0 + 0.3402777778 Combine like terms: -0.3402777778 + 0.3402777778 = 0.0000000000 0.0000000000 + -1.166666667a + a2 = 0 + 0.3402777778 -1.166666667a + a2 = 0 + 0.3402777778 Combine like terms: 0 + 0.3402777778 = 0.3402777778 -1.166666667a + a2 = 0.3402777778 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 = 0.3402777778 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667a + a2 = 0.3402777778 + 0.3402777780 Combine like terms: 0.3402777778 + 0.3402777780 = 0.6805555558 0.3402777780 + -1.166666667a + a2 = 0.6805555558 Factor a perfect square on the left side: (a + -0.5833333335)(a + -0.5833333335) = 0.6805555558 Calculate the square root of the right side: 0.824957912 Break this problem into two subproblems by setting (a + -0.5833333335) equal to 0.824957912 and -0.824957912.Subproblem 1
a + -0.5833333335 = 0.824957912 Simplifying a + -0.5833333335 = 0.824957912 Reorder the terms: -0.5833333335 + a = 0.824957912 Solving -0.5833333335 + a = 0.824957912 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 = 0.824957912 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = 0.824957912 + 0.5833333335 a = 0.824957912 + 0.5833333335 Combine like terms: 0.824957912 + 0.5833333335 = 1.4082912455 a = 1.4082912455 Simplifying a = 1.4082912455Subproblem 2
a + -0.5833333335 = -0.824957912 Simplifying a + -0.5833333335 = -0.824957912 Reorder the terms: -0.5833333335 + a = -0.824957912 Solving -0.5833333335 + a = -0.824957912 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 = -0.824957912 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = -0.824957912 + 0.5833333335 a = -0.824957912 + 0.5833333335 Combine like terms: -0.824957912 + 0.5833333335 = -0.2416245785 a = -0.2416245785 Simplifying a = -0.2416245785Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.4082912455, -0.2416245785}
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