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Simplifying a2 + -17a + 12 = 0 Reorder the terms: 12 + -17a + a2 = 0 Solving 12 + -17a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -17a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + -17a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -17a + a2 = 0 + -12 -17a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 -17a + a2 = -12 The a term is -17a. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17a + 72.25 + a2 = -12 + 72.25 Reorder the terms: 72.25 + -17a + a2 = -12 + 72.25 Combine like terms: -12 + 72.25 = 60.25 72.25 + -17a + a2 = 60.25 Factor a perfect square on the left side: (a + -8.5)(a + -8.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (a + -8.5) equal to 7.762087348 and -7.762087348.Subproblem 1
a + -8.5 = 7.762087348 Simplifying a + -8.5 = 7.762087348 Reorder the terms: -8.5 + a = 7.762087348 Solving -8.5 + a = 7.762087348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + a = 7.762087348 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = 7.762087348 + 8.5 a = 7.762087348 + 8.5 Combine like terms: 7.762087348 + 8.5 = 16.262087348 a = 16.262087348 Simplifying a = 16.262087348Subproblem 2
a + -8.5 = -7.762087348 Simplifying a + -8.5 = -7.762087348 Reorder the terms: -8.5 + a = -7.762087348 Solving -8.5 + a = -7.762087348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + a = -7.762087348 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = -7.762087348 + 8.5 a = -7.762087348 + 8.5 Combine like terms: -7.762087348 + 8.5 = 0.737912652 a = 0.737912652 Simplifying a = 0.737912652Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.262087348, 0.737912652}
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