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Simplifying a2 + -550a = 58225.8 Reorder the terms: -550a + a2 = 58225.8 Solving -550a + a2 = 58225.8 Solving for variable 'a'. Reorder the terms: -58225.8 + -550a + a2 = 58225.8 + -58225.8 Combine like terms: 58225.8 + -58225.8 = 0.0 -58225.8 + -550a + a2 = 0.0 Begin completing the square. Move the constant term to the right: Add '58225.8' to each side of the equation. -58225.8 + -550a + 58225.8 + a2 = 0.0 + 58225.8 Reorder the terms: -58225.8 + 58225.8 + -550a + a2 = 0.0 + 58225.8 Combine like terms: -58225.8 + 58225.8 = 0.0 0.0 + -550a + a2 = 0.0 + 58225.8 -550a + a2 = 0.0 + 58225.8 Combine like terms: 0.0 + 58225.8 = 58225.8 -550a + a2 = 58225.8 The a term is -550a. Take half its coefficient (-275). Square it (75625) and add it to both sides. Add '75625' to each side of the equation. -550a + 75625 + a2 = 58225.8 + 75625 Reorder the terms: 75625 + -550a + a2 = 58225.8 + 75625 Combine like terms: 58225.8 + 75625 = 133850.8 75625 + -550a + a2 = 133850.8 Factor a perfect square on the left side: (a + -275)(a + -275) = 133850.8 Calculate the square root of the right side: 365.856255926 Break this problem into two subproblems by setting (a + -275) equal to 365.856255926 and -365.856255926.Subproblem 1
a + -275 = 365.856255926 Simplifying a + -275 = 365.856255926 Reorder the terms: -275 + a = 365.856255926 Solving -275 + a = 365.856255926 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '275' to each side of the equation. -275 + 275 + a = 365.856255926 + 275 Combine like terms: -275 + 275 = 0 0 + a = 365.856255926 + 275 a = 365.856255926 + 275 Combine like terms: 365.856255926 + 275 = 640.856255926 a = 640.856255926 Simplifying a = 640.856255926Subproblem 2
a + -275 = -365.856255926 Simplifying a + -275 = -365.856255926 Reorder the terms: -275 + a = -365.856255926 Solving -275 + a = -365.856255926 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '275' to each side of the equation. -275 + 275 + a = -365.856255926 + 275 Combine like terms: -275 + 275 = 0 0 + a = -365.856255926 + 275 a = -365.856255926 + 275 Combine like terms: -365.856255926 + 275 = -90.856255926 a = -90.856255926 Simplifying a = -90.856255926Solution
The solution to the problem is based on the solutions from the subproblems. a = {640.856255926, -90.856255926}
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