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Simplifying 0.5a2 + a + -40 = 0 Reorder the terms: -40 + a + 0.5a2 = 0 Solving -40 + a + 0.5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -80 + 2a + a2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 2a + 80 + a2 = 0 + 80 Reorder the terms: -80 + 80 + 2a + a2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 2a + a2 = 0 + 80 2a + a2 = 0 + 80 Combine like terms: 0 + 80 = 80 2a + a2 = 80 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. 2a + 0.25 + a2 = 80 + 0.25 Reorder the terms: 0.25 + 2a + a2 = 80 + 0.25 Combine like terms: 80 + 0.25 = 80.25 0.25 + 2a + a2 = 80.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (a + 0.5) equal to 8.958236434 and -8.958236434.Subproblem 1
a + 0.5 = 8.958236434 Simplifying a + 0.5 = 8.958236434 Reorder the terms: 0.5 + a = 8.958236434 Solving 0.5 + a = 8.958236434 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 = 8.958236434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 8.958236434 + -0.5 a = 8.958236434 + -0.5 Combine like terms: 8.958236434 + -0.5 = 8.458236434 a = 8.458236434 Simplifying a = 8.458236434Subproblem 2
a + 0.5 = -8.958236434 Simplifying a + 0.5 = -8.958236434 Reorder the terms: 0.5 + a = -8.958236434 Solving 0.5 + a = -8.958236434 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 = -8.958236434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -8.958236434 + -0.5 a = -8.958236434 + -0.5 Combine like terms: -8.958236434 + -0.5 = -9.458236434 a = -9.458236434 Simplifying a = -9.458236434Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.458236434, -9.458236434}
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