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Simplifying a2 + -200a + 8148 = 0 Reorder the terms: 8148 + -200a + a2 = 0 Solving 8148 + -200a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-8148' to each side of the equation. 8148 + -200a + -8148 + a2 = 0 + -8148 Reorder the terms: 8148 + -8148 + -200a + a2 = 0 + -8148 Combine like terms: 8148 + -8148 = 0 0 + -200a + a2 = 0 + -8148 -200a + a2 = 0 + -8148 Combine like terms: 0 + -8148 = -8148 -200a + a2 = -8148 The a term is -200a. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200a + 10000 + a2 = -8148 + 10000 Reorder the terms: 10000 + -200a + a2 = -8148 + 10000 Combine like terms: -8148 + 10000 = 1852 10000 + -200a + a2 = 1852 Factor a perfect square on the left side: (a + -100)(a + -100) = 1852 Calculate the square root of the right side: 43.034869583 Break this problem into two subproblems by setting (a + -100) equal to 43.034869583 and -43.034869583.Subproblem 1
a + -100 = 43.034869583 Simplifying a + -100 = 43.034869583 Reorder the terms: -100 + a = 43.034869583 Solving -100 + a = 43.034869583 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + a = 43.034869583 + 100 Combine like terms: -100 + 100 = 0 0 + a = 43.034869583 + 100 a = 43.034869583 + 100 Combine like terms: 43.034869583 + 100 = 143.034869583 a = 143.034869583 Simplifying a = 143.034869583Subproblem 2
a + -100 = -43.034869583 Simplifying a + -100 = -43.034869583 Reorder the terms: -100 + a = -43.034869583 Solving -100 + a = -43.034869583 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + a = -43.034869583 + 100 Combine like terms: -100 + 100 = 0 0 + a = -43.034869583 + 100 a = -43.034869583 + 100 Combine like terms: -43.034869583 + 100 = 56.965130417 a = 56.965130417 Simplifying a = 56.965130417Solution
The solution to the problem is based on the solutions from the subproblems. a = {143.034869583, 56.965130417}
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