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Simplifying a2 + 5a + -45 = 0 Reorder the terms: -45 + 5a + a2 = 0 Solving -45 + 5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 5a + 45 + a2 = 0 + 45 Reorder the terms: -45 + 45 + 5a + a2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 5a + a2 = 0 + 45 5a + a2 = 0 + 45 Combine like terms: 0 + 45 = 45 5a + a2 = 45 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 45 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 45 + 6.25 Combine like terms: 45 + 6.25 = 51.25 6.25 + 5a + a2 = 51.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (a + 2.5) equal to 7.158910532 and -7.158910532.Subproblem 1
a + 2.5 = 7.158910532 Simplifying a + 2.5 = 7.158910532 Reorder the terms: 2.5 + a = 7.158910532 Solving 2.5 + a = 7.158910532 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 7.158910532 + -2.5 a = 7.158910532 + -2.5 Combine like terms: 7.158910532 + -2.5 = 4.658910532 a = 4.658910532 Simplifying a = 4.658910532Subproblem 2
a + 2.5 = -7.158910532 Simplifying a + 2.5 = -7.158910532 Reorder the terms: 2.5 + a = -7.158910532 Solving 2.5 + a = -7.158910532 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -7.158910532 + -2.5 a = -7.158910532 + -2.5 Combine like terms: -7.158910532 + -2.5 = -9.658910532 a = -9.658910532 Simplifying a = -9.658910532Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.658910532, -9.658910532}
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