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Simplifying (0.654a2) + -1(1624a) + 3324 = 0 Remove parenthesis around (1624a) (0.654a2) + -1 * 1624a + 3324 = 0 Multiply -1 * 1624 (0.654a2) + -1624a + 3324 = 0 Reorder the terms: 3324 + -1624a + (0.654a2) = 0 Solving 3324 + -1624a + (0.654a2) = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.654 the coefficient of the squared term: Divide each side by '0.654'. 5082.568807 + -2483.180428a + a2 = 0 Move the constant term to the right: Add '-5082.568807' to each side of the equation. 5082.568807 + -2483.180428a + -5082.568807 + a2 = 0 + -5082.568807 Reorder the terms: 5082.568807 + -5082.568807 + -2483.180428a + a2 = 0 + -5082.568807 Combine like terms: 5082.568807 + -5082.568807 = 0.000000 0.000000 + -2483.180428a + a2 = 0 + -5082.568807 -2483.180428a + a2 = 0 + -5082.568807 Combine like terms: 0 + -5082.568807 = -5082.568807 -2483.180428a + a2 = -5082.568807 The a term is -2483.180428a. Take half its coefficient (-1241.590214). Square it (1541546.260) and add it to both sides. Add '1541546.260' to each side of the equation. -2483.180428a + 1541546.260 + a2 = -5082.568807 + 1541546.260 Reorder the terms: 1541546.260 + -2483.180428a + a2 = -5082.568807 + 1541546.260 Combine like terms: -5082.568807 + 1541546.260 = 1536463.691193 1541546.260 + -2483.180428a + a2 = 1536463.691193 Factor a perfect square on the left side: ((a) + -1241.590214)((a) + -1241.590214) = 1536463.691193 Calculate the square root of the right side: 1239.541726282 Break this problem into two subproblems by setting ((a) + -1241.590214) equal to 1239.541726282 and -1239.541726282.Subproblem 1
(a) + -1241.590214 = 1239.541726282 Simplifying (a) + -1241.590214 = 1239.541726282 a + -1241.590214 = 1239.541726282 Reorder the terms: -1241.590214 + a = 1239.541726282 Solving -1241.590214 + a = 1239.541726282 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1241.590214' to each side of the equation. -1241.590214 + 1241.590214 + a = 1239.541726282 + 1241.590214 Combine like terms: -1241.590214 + 1241.590214 = 0.000000 0.000000 + a = 1239.541726282 + 1241.590214 a = 1239.541726282 + 1241.590214 Combine like terms: 1239.541726282 + 1241.590214 = 2481.131940282 a = 2481.131940282 Simplifying a = 2481.131940282Subproblem 2
(a) + -1241.590214 = -1239.541726282 Simplifying (a) + -1241.590214 = -1239.541726282 a + -1241.590214 = -1239.541726282 Reorder the terms: -1241.590214 + a = -1239.541726282 Solving -1241.590214 + a = -1239.541726282 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1241.590214' to each side of the equation. -1241.590214 + 1241.590214 + a = -1239.541726282 + 1241.590214 Combine like terms: -1241.590214 + 1241.590214 = 0.000000 0.000000 + a = -1239.541726282 + 1241.590214 a = -1239.541726282 + 1241.590214 Combine like terms: -1239.541726282 + 1241.590214 = 2.048487718 a = 2.048487718 Simplifying a = 2.048487718Solution
The solution to the problem is based on the solutions from the subproblems. a = {2481.131940282, 2.048487718}
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