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Simplifying a2 + -900a + 47291.83 = 0 Reorder the terms: 47291.83 + -900a + a2 = 0 Solving 47291.83 + -900a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-47291.83' to each side of the equation. 47291.83 + -900a + -47291.83 + a2 = 0 + -47291.83 Reorder the terms: 47291.83 + -47291.83 + -900a + a2 = 0 + -47291.83 Combine like terms: 47291.83 + -47291.83 = 0.00 0.00 + -900a + a2 = 0 + -47291.83 -900a + a2 = 0 + -47291.83 Combine like terms: 0 + -47291.83 = -47291.83 -900a + a2 = -47291.83 The a term is -900a. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900a + 202500 + a2 = -47291.83 + 202500 Reorder the terms: 202500 + -900a + a2 = -47291.83 + 202500 Combine like terms: -47291.83 + 202500 = 155208.17 202500 + -900a + a2 = 155208.17 Factor a perfect square on the left side: (a + -450)(a + -450) = 155208.17 Calculate the square root of the right side: 393.964681158 Break this problem into two subproblems by setting (a + -450) equal to 393.964681158 and -393.964681158.Subproblem 1
a + -450 = 393.964681158 Simplifying a + -450 = 393.964681158 Reorder the terms: -450 + a = 393.964681158 Solving -450 + a = 393.964681158 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + a = 393.964681158 + 450 Combine like terms: -450 + 450 = 0 0 + a = 393.964681158 + 450 a = 393.964681158 + 450 Combine like terms: 393.964681158 + 450 = 843.964681158 a = 843.964681158 Simplifying a = 843.964681158Subproblem 2
a + -450 = -393.964681158 Simplifying a + -450 = -393.964681158 Reorder the terms: -450 + a = -393.964681158 Solving -450 + a = -393.964681158 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + a = -393.964681158 + 450 Combine like terms: -450 + 450 = 0 0 + a = -393.964681158 + 450 a = -393.964681158 + 450 Combine like terms: -393.964681158 + 450 = 56.035318842 a = 56.035318842 Simplifying a = 56.035318842Solution
The solution to the problem is based on the solutions from the subproblems. a = {843.964681158, 56.035318842}
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