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Simplifying a2 + -17a = 12 Reorder the terms: -17a + a2 = 12 Solving -17a + a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + -17a + a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -17a + a2 = 0 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 = 84.25 72.25 + -17a + a2 = 84.25 Factor a perfect square on the left side: (a + -8.5)(a + -8.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (a + -8.5) equal to 9.178779875 and -9.178779875.Subproblem 1
a + -8.5 = 9.178779875 Simplifying a + -8.5 = 9.178779875 Reorder the terms: -8.5 + a = 9.178779875 Solving -8.5 + a = 9.178779875 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 = 9.178779875 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = 9.178779875 + 8.5 a = 9.178779875 + 8.5 Combine like terms: 9.178779875 + 8.5 = 17.678779875 a = 17.678779875 Simplifying a = 17.678779875Subproblem 2
a + -8.5 = -9.178779875 Simplifying a + -8.5 = -9.178779875 Reorder the terms: -8.5 + a = -9.178779875 Solving -8.5 + a = -9.178779875 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 = -9.178779875 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + a = -9.178779875 + 8.5 a = -9.178779875 + 8.5 Combine like terms: -9.178779875 + 8.5 = -0.678779875 a = -0.678779875 Simplifying a = -0.678779875Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.678779875, -0.678779875}
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