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Simplifying 0 = a2 + -6a + 7 Reorder the terms: 0 = 7 + -6a + a2 Solving 0 = 7 + -6a + a2 Solving for variable 'a'. Combine like terms: 0 + -7 = -7 -7 + 6a + -1a2 = 7 + -6a + a2 + -7 + 6a + -1a2 Reorder the terms: -7 + 6a + -1a2 = 7 + -7 + -6a + 6a + a2 + -1a2 Combine like terms: 7 + -7 = 0 -7 + 6a + -1a2 = 0 + -6a + 6a + a2 + -1a2 -7 + 6a + -1a2 = -6a + 6a + a2 + -1a2 Combine like terms: -6a + 6a = 0 -7 + 6a + -1a2 = 0 + a2 + -1a2 -7 + 6a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -7 + 6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -6a + a2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6a + -7 + a2 = 0 + -7 Reorder the terms: 7 + -7 + -6a + a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6a + a2 = 0 + -7 -6a + a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6a + a2 = -7 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = -7 + 9 Reorder the terms: 9 + -6a + a2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6a + a2 = 2 Factor a perfect square on the left side: (a + -3)(a + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (a + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
a + -3 = 1.414213562 Simplifying a + -3 = 1.414213562 Reorder the terms: -3 + a = 1.414213562 Solving -3 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + a = 1.414213562 + 3 a = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 a = 4.414213562 Simplifying a = 4.414213562Subproblem 2
a + -3 = -1.414213562 Simplifying a + -3 = -1.414213562 Reorder the terms: -3 + a = -1.414213562 Solving -3 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + a = -1.414213562 + 3 a = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 a = 1.585786438 Simplifying a = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.414213562, 1.585786438}
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