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Simplifying a2 + 6a + -13 = -9 Reorder the terms: -13 + 6a + a2 = -9 Solving -13 + 6a + a2 = -9 Solving for variable 'a'. Reorder the terms: -13 + 9 + 6a + a2 = -9 + 9 Combine like terms: -13 + 9 = -4 -4 + 6a + a2 = -9 + 9 Combine like terms: -9 + 9 = 0 -4 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 6a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6a + a2 = 0 + 4 6a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 6a + a2 = 4 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 = 4 + 9 Reorder the terms: 9 + 6a + a2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6a + a2 = 13 Factor a perfect square on the left side: (a + 3)(a + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (a + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
a + 3 = 3.605551275 Simplifying a + 3 = 3.605551275 Reorder the terms: 3 + a = 3.605551275 Solving 3 + a = 3.605551275 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 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.605551275 + -3 a = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 a = 0.605551275 Simplifying a = 0.605551275Subproblem 2
a + 3 = -3.605551275 Simplifying a + 3 = -3.605551275 Reorder the terms: 3 + a = -3.605551275 Solving 3 + a = -3.605551275 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 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.605551275 + -3 a = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 a = -6.605551275 Simplifying a = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.605551275, -6.605551275}
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