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Simplifying (a2 * -0.669) + (a * 32.8) + 2998 = 0 Reorder the terms for easier multiplication: (-0.669a2) + (a * 32.8) + 2998 = 0 Reorder the terms for easier multiplication: (-0.669a2) + (32.8a) + 2998 = 0 Reorder the terms: 2998 + (32.8a) + (-0.669a2) = 0 Solving 2998 + (32.8a) + (-0.669a2) = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -0.669 the coefficient of the squared term: Divide each side by '-0.669'. -4481.315396 + (-49.0284006a) + a2 = 0 Move the constant term to the right: Add '4481.315396' to each side of the equation. -4481.315396 + (-49.0284006a) + 4481.315396 + a2 = 0 + 4481.315396 Reorder the terms: -4481.315396 + 4481.315396 + (-49.0284006a) + a2 = 0 + 4481.315396 Combine like terms: -4481.315396 + 4481.315396 = 0.000000 0.000000 + (-49.0284006a) + a2 = 0 + 4481.315396 (-49.0284006a) + a2 = 0 + 4481.315396 Combine like terms: 0 + 4481.315396 = 4481.315396 (-49.0284006a) + a2 = 4481.315396 The a term is (-49.0284006a). Take half its coefficient (-24.5142003). Square it (600.9460163) and add it to both sides. Add '600.9460163' to each side of the equation. (-49.0284006a) + 600.9460163 + a2 = 4481.315396 + 600.9460163 Reorder the terms: 600.9460163 + (-49.0284006a) + a2 = 4481.315396 + 600.9460163 Combine like terms: 4481.315396 + 600.9460163 = 5082.2614123 600.9460163 + (-49.0284006a) + a2 = 5082.2614123 Factor a perfect square on the left side: ((a) + -24.5142003)((a) + -24.5142003) = 5082.2614123 Calculate the square root of the right side: 71.28998115 Break this problem into two subproblems by setting ((a) + -24.5142003) equal to 71.28998115 and -71.28998115.Subproblem 1
(a) + -24.5142003 = 71.28998115 Simplifying (a) + -24.5142003 = 71.28998115 a + -24.5142003 = 71.28998115 Reorder the terms: -24.5142003 + a = 71.28998115 Solving -24.5142003 + a = 71.28998115 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '24.5142003' to each side of the equation. -24.5142003 + 24.5142003 + a = 71.28998115 + 24.5142003 Combine like terms: -24.5142003 + 24.5142003 = 0.0000000 0.0000000 + a = 71.28998115 + 24.5142003 a = 71.28998115 + 24.5142003 Combine like terms: 71.28998115 + 24.5142003 = 95.80418145 a = 95.80418145 Simplifying a = 95.80418145Subproblem 2
(a) + -24.5142003 = -71.28998115 Simplifying (a) + -24.5142003 = -71.28998115 a + -24.5142003 = -71.28998115 Reorder the terms: -24.5142003 + a = -71.28998115 Solving -24.5142003 + a = -71.28998115 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '24.5142003' to each side of the equation. -24.5142003 + 24.5142003 + a = -71.28998115 + 24.5142003 Combine like terms: -24.5142003 + 24.5142003 = 0.0000000 0.0000000 + a = -71.28998115 + 24.5142003 a = -71.28998115 + 24.5142003 Combine like terms: -71.28998115 + 24.5142003 = -46.77578085 a = -46.77578085 Simplifying a = -46.77578085Solution
The solution to the problem is based on the solutions from the subproblems. a = {95.80418145, -46.77578085}
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