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Simplifying 400a + -1a2 = 15846.47 Solving 400a + -1a2 = 15846.47 Solving for variable 'a'. Reorder the terms: -15846.47 + 400a + -1a2 = 15846.47 + -15846.47 Combine like terms: 15846.47 + -15846.47 = 0.00 -15846.47 + 400a + -1a2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15846.47 + -400a + a2 = 0.00 Move the constant term to the right: Add '-15846.47' to each side of the equation. 15846.47 + -400a + -15846.47 + a2 = 0.00 + -15846.47 Reorder the terms: 15846.47 + -15846.47 + -400a + a2 = 0.00 + -15846.47 Combine like terms: 15846.47 + -15846.47 = 0.00 0.00 + -400a + a2 = 0.00 + -15846.47 -400a + a2 = 0.00 + -15846.47 Combine like terms: 0.00 + -15846.47 = -15846.47 -400a + a2 = -15846.47 The a term is -400a. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400a + 40000 + a2 = -15846.47 + 40000 Reorder the terms: 40000 + -400a + a2 = -15846.47 + 40000 Combine like terms: -15846.47 + 40000 = 24153.53 40000 + -400a + a2 = 24153.53 Factor a perfect square on the left side: (a + -200)(a + -200) = 24153.53 Calculate the square root of the right side: 155.414059853 Break this problem into two subproblems by setting (a + -200) equal to 155.414059853 and -155.414059853.Subproblem 1
a + -200 = 155.414059853 Simplifying a + -200 = 155.414059853 Reorder the terms: -200 + a = 155.414059853 Solving -200 + a = 155.414059853 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + a = 155.414059853 + 200 Combine like terms: -200 + 200 = 0 0 + a = 155.414059853 + 200 a = 155.414059853 + 200 Combine like terms: 155.414059853 + 200 = 355.414059853 a = 355.414059853 Simplifying a = 355.414059853Subproblem 2
a + -200 = -155.414059853 Simplifying a + -200 = -155.414059853 Reorder the terms: -200 + a = -155.414059853 Solving -200 + a = -155.414059853 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + a = -155.414059853 + 200 Combine like terms: -200 + 200 = 0 0 + a = -155.414059853 + 200 a = -155.414059853 + 200 Combine like terms: -155.414059853 + 200 = 44.585940147 a = 44.585940147 Simplifying a = 44.585940147Solution
The solution to the problem is based on the solutions from the subproblems. a = {355.414059853, 44.585940147}
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