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Simplifying 18a2 + 21a + 4 = 0 Reorder the terms: 4 + 21a + 18a2 = 0 Solving 4 + 21a + 18a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2222222222 + 1.166666667a + a2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 1.166666667a + -0.2222222222 + a2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 1.166666667a + a2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 1.166666667a + a2 = 0 + -0.2222222222 1.166666667a + a2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 1.166666667a + a2 = -0.2222222222 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 = -0.2222222222 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667a + a2 = -0.2222222222 + 0.3402777780 Combine like terms: -0.2222222222 + 0.3402777780 = 0.1180555558 0.3402777780 + 1.166666667a + a2 = 0.1180555558 Factor a perfect square on the left side: (a + 0.5833333335)(a + 0.5833333335) = 0.1180555558 Calculate the square root of the right side: 0.343592136 Break this problem into two subproblems by setting (a + 0.5833333335) equal to 0.343592136 and -0.343592136.Subproblem 1
a + 0.5833333335 = 0.343592136 Simplifying a + 0.5833333335 = 0.343592136 Reorder the terms: 0.5833333335 + a = 0.343592136 Solving 0.5833333335 + a = 0.343592136 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 = 0.343592136 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + a = 0.343592136 + -0.5833333335 a = 0.343592136 + -0.5833333335 Combine like terms: 0.343592136 + -0.5833333335 = -0.2397411975 a = -0.2397411975 Simplifying a = -0.2397411975Subproblem 2
a + 0.5833333335 = -0.343592136 Simplifying a + 0.5833333335 = -0.343592136 Reorder the terms: 0.5833333335 + a = -0.343592136 Solving 0.5833333335 + a = -0.343592136 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 = -0.343592136 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + a = -0.343592136 + -0.5833333335 a = -0.343592136 + -0.5833333335 Combine like terms: -0.343592136 + -0.5833333335 = -0.9269254695 a = -0.9269254695 Simplifying a = -0.9269254695Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.2397411975, -0.9269254695}
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