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Simplifying -5a2 + a + 344 = 0 Reorder the terms: 344 + a + -5a2 = 0 Solving 344 + a + -5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -68.8 + -0.2a + a2 = 0 Move the constant term to the right: Add '68.8' to each side of the equation. -68.8 + -0.2a + 68.8 + a2 = 0 + 68.8 Reorder the terms: -68.8 + 68.8 + -0.2a + a2 = 0 + 68.8 Combine like terms: -68.8 + 68.8 = 0.0 0.0 + -0.2a + a2 = 0 + 68.8 -0.2a + a2 = 0 + 68.8 Combine like terms: 0 + 68.8 = 68.8 -0.2a + a2 = 68.8 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. -0.2a + 0.25 + a2 = 68.8 + 0.25 Reorder the terms: 0.25 + -0.2a + a2 = 68.8 + 0.25 Combine like terms: 68.8 + 0.25 = 69.05 0.25 + -0.2a + a2 = 69.05 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 69.05 Calculate the square root of the right side: 8.309632964 Break this problem into two subproblems by setting (a + 0.5) equal to 8.309632964 and -8.309632964.Subproblem 1
a + 0.5 = 8.309632964 Simplifying a + 0.5 = 8.309632964 Reorder the terms: 0.5 + a = 8.309632964 Solving 0.5 + a = 8.309632964 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 = 8.309632964 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 8.309632964 + -0.5 a = 8.309632964 + -0.5 Combine like terms: 8.309632964 + -0.5 = 7.809632964 a = 7.809632964 Simplifying a = 7.809632964Subproblem 2
a + 0.5 = -8.309632964 Simplifying a + 0.5 = -8.309632964 Reorder the terms: 0.5 + a = -8.309632964 Solving 0.5 + a = -8.309632964 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 = -8.309632964 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -8.309632964 + -0.5 a = -8.309632964 + -0.5 Combine like terms: -8.309632964 + -0.5 = -8.809632964 a = -8.809632964 Simplifying a = -8.809632964Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.809632964, -8.809632964}
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