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Simplifying a2 + 13a + 8 = 0 Reorder the terms: 8 + 13a + a2 = 0 Solving 8 + 13a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 13a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + 13a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 13a + a2 = 0 + -8 13a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 13a + a2 = -8 The a term is 13a. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13a + 42.25 + a2 = -8 + 42.25 Reorder the terms: 42.25 + 13a + a2 = -8 + 42.25 Combine like terms: -8 + 42.25 = 34.25 42.25 + 13a + a2 = 34.25 Factor a perfect square on the left side: (a + 6.5)(a + 6.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (a + 6.5) equal to 5.852349955 and -5.852349955.Subproblem 1
a + 6.5 = 5.852349955 Simplifying a + 6.5 = 5.852349955 Reorder the terms: 6.5 + a = 5.852349955 Solving 6.5 + a = 5.852349955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 5.852349955 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 5.852349955 + -6.5 a = 5.852349955 + -6.5 Combine like terms: 5.852349955 + -6.5 = -0.647650045 a = -0.647650045 Simplifying a = -0.647650045Subproblem 2
a + 6.5 = -5.852349955 Simplifying a + 6.5 = -5.852349955 Reorder the terms: 6.5 + a = -5.852349955 Solving 6.5 + a = -5.852349955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -5.852349955 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -5.852349955 + -6.5 a = -5.852349955 + -6.5 Combine like terms: -5.852349955 + -6.5 = -12.352349955 a = -12.352349955 Simplifying a = -12.352349955Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.647650045, -12.352349955}
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