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Simplifying 2a2 + 2a + -99 = 0 Reorder the terms: -99 + 2a + 2a2 = 0 Solving -99 + 2a + 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'. -49.5 + a + a2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + a + 49.5 + a2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + a + a2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + a + a2 = 0 + 49.5 a + a2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 a + a2 = 49.5 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 49.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 49.5 + 0.25 Combine like terms: 49.5 + 0.25 = 49.75 1.25 + a2 = 49.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (a + 0.5) equal to 7.05336799 and -7.05336799.Subproblem 1
a + 0.5 = 7.05336799 Simplifying a + 0.5 = 7.05336799 Reorder the terms: 0.5 + a = 7.05336799 Solving 0.5 + a = 7.05336799 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 7.05336799 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 7.05336799 + -0.5 a = 7.05336799 + -0.5 Combine like terms: 7.05336799 + -0.5 = 6.55336799 a = 6.55336799 Simplifying a = 6.55336799Subproblem 2
a + 0.5 = -7.05336799 Simplifying a + 0.5 = -7.05336799 Reorder the terms: 0.5 + a = -7.05336799 Solving 0.5 + a = -7.05336799 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -7.05336799 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -7.05336799 + -0.5 a = -7.05336799 + -0.5 Combine like terms: -7.05336799 + -0.5 = -7.55336799 a = -7.55336799 Simplifying a = -7.55336799Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.55336799, -7.55336799}
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