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Simplifying 2640.6 = 96.965X2 + -13209X + 451022 Reorder the terms: 2640.6 = 451022 + -13209X + 96.965X2 Solving 2640.6 = 451022 + -13209X + 96.965X2 Solving for variable 'X'. Combine like terms: 2640.6 + -451022 = -448381.4 -448381.4 + 13209X + -96.965X2 = 451022 + -13209X + 96.965X2 + -451022 + 13209X + -96.965X2 Reorder the terms: -448381.4 + 13209X + -96.965X2 = 451022 + -451022 + -13209X + 13209X + 96.965X2 + -96.965X2 Combine like terms: 451022 + -451022 = 0 -448381.4 + 13209X + -96.965X2 = 0 + -13209X + 13209X + 96.965X2 + -96.965X2 -448381.4 + 13209X + -96.965X2 = -13209X + 13209X + 96.965X2 + -96.965X2 Combine like terms: -13209X + 13209X = 0 -448381.4 + 13209X + -96.965X2 = 0 + 96.965X2 + -96.965X2 -448381.4 + 13209X + -96.965X2 = 96.965X2 + -96.965X2 Combine like terms: 96.965X2 + -96.965X2 = 0.000 -448381.4 + 13209X + -96.965X2 = 0.000 Begin completing the square. Divide all terms by -96.965 the coefficient of the squared term: Divide each side by '-96.965'. 4624.15717 + -136.2244109X + X2 = 0 Move the constant term to the right: Add '-4624.15717' to each side of the equation. 4624.15717 + -136.2244109X + -4624.15717 + X2 = 0 + -4624.15717 Reorder the terms: 4624.15717 + -4624.15717 + -136.2244109X + X2 = 0 + -4624.15717 Combine like terms: 4624.15717 + -4624.15717 = 0.00000 0.00000 + -136.2244109X + X2 = 0 + -4624.15717 -136.2244109X + X2 = 0 + -4624.15717 Combine like terms: 0 + -4624.15717 = -4624.15717 -136.2244109X + X2 = -4624.15717 The X term is -136.2244109X. Take half its coefficient (-68.11220545). Square it (4639.272531) and add it to both sides. Add '4639.272531' to each side of the equation. -136.2244109X + 4639.272531 + X2 = -4624.15717 + 4639.272531 Reorder the terms: 4639.272531 + -136.2244109X + X2 = -4624.15717 + 4639.272531 Combine like terms: -4624.15717 + 4639.272531 = 15.115361 4639.272531 + -136.2244109X + X2 = 15.115361 Factor a perfect square on the left side: (X + -68.11220545)(X + -68.11220545) = 15.115361 Calculate the square root of the right side: 3.887847862 Break this problem into two subproblems by setting (X + -68.11220545) equal to 3.887847862 and -3.887847862.Subproblem 1
X + -68.11220545 = 3.887847862 Simplifying X + -68.11220545 = 3.887847862 Reorder the terms: -68.11220545 + X = 3.887847862 Solving -68.11220545 + X = 3.887847862 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '68.11220545' to each side of the equation. -68.11220545 + 68.11220545 + X = 3.887847862 + 68.11220545 Combine like terms: -68.11220545 + 68.11220545 = 0.00000000 0.00000000 + X = 3.887847862 + 68.11220545 X = 3.887847862 + 68.11220545 Combine like terms: 3.887847862 + 68.11220545 = 72.000053312 X = 72.000053312 Simplifying X = 72.000053312Subproblem 2
X + -68.11220545 = -3.887847862 Simplifying X + -68.11220545 = -3.887847862 Reorder the terms: -68.11220545 + X = -3.887847862 Solving -68.11220545 + X = -3.887847862 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '68.11220545' to each side of the equation. -68.11220545 + 68.11220545 + X = -3.887847862 + 68.11220545 Combine like terms: -68.11220545 + 68.11220545 = 0.00000000 0.00000000 + X = -3.887847862 + 68.11220545 X = -3.887847862 + 68.11220545 Combine like terms: -3.887847862 + 68.11220545 = 64.224357588 X = 64.224357588 Simplifying X = 64.224357588Solution
The solution to the problem is based on the solutions from the subproblems. X = {72.000053312, 64.224357588}
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