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Simplifying a2 + 6a + -13 = 0 Reorder the terms: -13 + 6a + a2 = 0 Solving -13 + 6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 6a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + 6a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6a + a2 = 0 + 13 6a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 6a + a2 = 13 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 = 13 + 9 Reorder the terms: 9 + 6a + a2 = 13 + 9 Combine like terms: 13 + 9 = 22 9 + 6a + a2 = 22 Factor a perfect square on the left side: (a + 3)(a + 3) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (a + 3) equal to 4.69041576 and -4.69041576.Subproblem 1
a + 3 = 4.69041576 Simplifying a + 3 = 4.69041576 Reorder the terms: 3 + a = 4.69041576 Solving 3 + a = 4.69041576 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 = 4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + a = 4.69041576 + -3 a = 4.69041576 + -3 Combine like terms: 4.69041576 + -3 = 1.69041576 a = 1.69041576 Simplifying a = 1.69041576Subproblem 2
a + 3 = -4.69041576 Simplifying a + 3 = -4.69041576 Reorder the terms: 3 + a = -4.69041576 Solving 3 + a = -4.69041576 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 = -4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + a = -4.69041576 + -3 a = -4.69041576 + -3 Combine like terms: -4.69041576 + -3 = -7.69041576 a = -7.69041576 Simplifying a = -7.69041576Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.69041576, -7.69041576}
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