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Simplifying 4193.64a2 + 28053.6a + -32070500 = 0 Reorder the terms: -32070500 + 28053.6a + 4193.64a2 = 0 Solving -32070500 + 28053.6a + 4193.64a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4193.64 the coefficient of the squared term: Divide each side by '4193.64'. -7647.413703 + 6.689558474a + a2 = 0 Move the constant term to the right: Add '7647.413703' to each side of the equation. -7647.413703 + 6.689558474a + 7647.413703 + a2 = 0 + 7647.413703 Reorder the terms: -7647.413703 + 7647.413703 + 6.689558474a + a2 = 0 + 7647.413703 Combine like terms: -7647.413703 + 7647.413703 = 0.000000 0.000000 + 6.689558474a + a2 = 0 + 7647.413703 6.689558474a + a2 = 0 + 7647.413703 Combine like terms: 0 + 7647.413703 = 7647.413703 6.689558474a + a2 = 7647.413703 The a term is 6.689558474a. Take half its coefficient (3.344779237). Square it (11.18754814) and add it to both sides. Add '11.18754814' to each side of the equation. 6.689558474a + 11.18754814 + a2 = 7647.413703 + 11.18754814 Reorder the terms: 11.18754814 + 6.689558474a + a2 = 7647.413703 + 11.18754814 Combine like terms: 7647.413703 + 11.18754814 = 7658.60125114 11.18754814 + 6.689558474a + a2 = 7658.60125114 Factor a perfect square on the left side: (a + 3.344779237)(a + 3.344779237) = 7658.60125114 Calculate the square root of the right side: 87.513434689 Break this problem into two subproblems by setting (a + 3.344779237) equal to 87.513434689 and -87.513434689.Subproblem 1
a + 3.344779237 = 87.513434689 Simplifying a + 3.344779237 = 87.513434689 Reorder the terms: 3.344779237 + a = 87.513434689 Solving 3.344779237 + a = 87.513434689 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.344779237' to each side of the equation. 3.344779237 + -3.344779237 + a = 87.513434689 + -3.344779237 Combine like terms: 3.344779237 + -3.344779237 = 0.000000000 0.000000000 + a = 87.513434689 + -3.344779237 a = 87.513434689 + -3.344779237 Combine like terms: 87.513434689 + -3.344779237 = 84.168655452 a = 84.168655452 Simplifying a = 84.168655452Subproblem 2
a + 3.344779237 = -87.513434689 Simplifying a + 3.344779237 = -87.513434689 Reorder the terms: 3.344779237 + a = -87.513434689 Solving 3.344779237 + a = -87.513434689 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.344779237' to each side of the equation. 3.344779237 + -3.344779237 + a = -87.513434689 + -3.344779237 Combine like terms: 3.344779237 + -3.344779237 = 0.000000000 0.000000000 + a = -87.513434689 + -3.344779237 a = -87.513434689 + -3.344779237 Combine like terms: -87.513434689 + -3.344779237 = -90.858213926 a = -90.858213926 Simplifying a = -90.858213926Solution
The solution to the problem is based on the solutions from the subproblems. a = {84.168655452, -90.858213926}
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