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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 = 17399.2 75625 + -550a + a2 = 17399.2 Factor a perfect square on the left side: (a + -275)(a + -275) = 17399.2 Calculate the square root of the right side: 131.906027156 Break this problem into two subproblems by setting (a + -275) equal to 131.906027156 and -131.906027156.Subproblem 1
a + -275 = 131.906027156 Simplifying a + -275 = 131.906027156 Reorder the terms: -275 + a = 131.906027156 Solving -275 + a = 131.906027156 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 = 131.906027156 + 275 Combine like terms: -275 + 275 = 0 0 + a = 131.906027156 + 275 a = 131.906027156 + 275 Combine like terms: 131.906027156 + 275 = 406.906027156 a = 406.906027156 Simplifying a = 406.906027156Subproblem 2
a + -275 = -131.906027156 Simplifying a + -275 = -131.906027156 Reorder the terms: -275 + a = -131.906027156 Solving -275 + a = -131.906027156 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 = -131.906027156 + 275 Combine like terms: -275 + 275 = 0 0 + a = -131.906027156 + 275 a = -131.906027156 + 275 Combine like terms: -131.906027156 + 275 = 143.093972844 a = 143.093972844 Simplifying a = 143.093972844Solution
The solution to the problem is based on the solutions from the subproblems. a = {406.906027156, 143.093972844}
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