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Simplifying a(a + -8) = 17 + -1a Reorder the terms: a(-8 + a) = 17 + -1a (-8 * a + a * a) = 17 + -1a (-8a + a2) = 17 + -1a Solving -8a + a2 = 17 + -1a Solving for variable 'a'. Reorder the terms: -17 + -8a + a + a2 = 17 + -1a + -17 + a Combine like terms: -8a + a = -7a -17 + -7a + a2 = 17 + -1a + -17 + a Reorder the terms: -17 + -7a + a2 = 17 + -17 + -1a + a Combine like terms: 17 + -17 = 0 -17 + -7a + a2 = 0 + -1a + a -17 + -7a + a2 = -1a + a Combine like terms: -1a + a = 0 -17 + -7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -7a + 17 + a2 = 0 + 17 Reorder the terms: -17 + 17 + -7a + a2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -7a + a2 = 0 + 17 -7a + a2 = 0 + 17 Combine like terms: 0 + 17 = 17 -7a + a2 = 17 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 17 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 17 + 12.25 Combine like terms: 17 + 12.25 = 29.25 12.25 + -7a + a2 = 29.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (a + -3.5) equal to 5.408326913 and -5.408326913.Subproblem 1
a + -3.5 = 5.408326913 Simplifying a + -3.5 = 5.408326913 Reorder the terms: -3.5 + a = 5.408326913 Solving -3.5 + a = 5.408326913 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 5.408326913 + 3.5 a = 5.408326913 + 3.5 Combine like terms: 5.408326913 + 3.5 = 8.908326913 a = 8.908326913 Simplifying a = 8.908326913Subproblem 2
a + -3.5 = -5.408326913 Simplifying a + -3.5 = -5.408326913 Reorder the terms: -3.5 + a = -5.408326913 Solving -3.5 + a = -5.408326913 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -5.408326913 + 3.5 a = -5.408326913 + 3.5 Combine like terms: -5.408326913 + 3.5 = -1.908326913 a = -1.908326913 Simplifying a = -1.908326913Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.908326913, -1.908326913}
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