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Simplifying a2 + -8a + 14 = 0 Reorder the terms: 14 + -8a + a2 = 0 Solving 14 + -8a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8a + -14 + a2 = 0 + -14 Reorder the terms: 14 + -14 + -8a + a2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8a + a2 = 0 + -14 -8a + a2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8a + a2 = -14 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -14 + 16 Reorder the terms: 16 + -8a + a2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8a + a2 = 2 Factor a perfect square on the left side: (a + -4)(a + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (a + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
a + -4 = 1.414213562 Simplifying a + -4 = 1.414213562 Reorder the terms: -4 + a = 1.414213562 Solving -4 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + a = 1.414213562 + 4 a = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 a = 5.414213562 Simplifying a = 5.414213562Subproblem 2
a + -4 = -1.414213562 Simplifying a + -4 = -1.414213562 Reorder the terms: -4 + a = -1.414213562 Solving -4 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + a = -1.414213562 + 4 a = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 a = 2.585786438 Simplifying a = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.414213562, 2.585786438}
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