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Simplifying 2a2 + 6a + -95 = 0 Reorder the terms: -95 + 6a + 2a2 = 0 Solving -95 + 6a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -47.5 + 3a + a2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + 3a + 47.5 + a2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + 3a + a2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + 3a + a2 = 0 + 47.5 3a + a2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 3a + a2 = 47.5 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 47.5 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 47.5 + 2.25 Combine like terms: 47.5 + 2.25 = 49.75 2.25 + 3a + a2 = 49.75 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (a + 1.5) equal to 7.05336799 and -7.05336799.Subproblem 1
a + 1.5 = 7.05336799 Simplifying a + 1.5 = 7.05336799 Reorder the terms: 1.5 + a = 7.05336799 Solving 1.5 + a = 7.05336799 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 7.05336799 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 7.05336799 + -1.5 a = 7.05336799 + -1.5 Combine like terms: 7.05336799 + -1.5 = 5.55336799 a = 5.55336799 Simplifying a = 5.55336799Subproblem 2
a + 1.5 = -7.05336799 Simplifying a + 1.5 = -7.05336799 Reorder the terms: 1.5 + a = -7.05336799 Solving 1.5 + a = -7.05336799 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -7.05336799 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -7.05336799 + -1.5 a = -7.05336799 + -1.5 Combine like terms: -7.05336799 + -1.5 = -8.55336799 a = -8.55336799 Simplifying a = -8.55336799Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.55336799, -8.55336799}
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