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Simplifying X2 + 112.5X = 446 Reorder the terms: 112.5X + X2 = 446 Solving 112.5X + X2 = 446 Solving for variable 'X'. Reorder the terms: -446 + 112.5X + X2 = 446 + -446 Combine like terms: 446 + -446 = 0 -446 + 112.5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '446' to each side of the equation. -446 + 112.5X + 446 + X2 = 0 + 446 Reorder the terms: -446 + 446 + 112.5X + X2 = 0 + 446 Combine like terms: -446 + 446 = 0 0 + 112.5X + X2 = 0 + 446 112.5X + X2 = 0 + 446 Combine like terms: 0 + 446 = 446 112.5X + X2 = 446 The X term is 112.5X. Take half its coefficient (56.25). Square it (3164.0625) and add it to both sides. Add '3164.0625' to each side of the equation. 112.5X + 3164.0625 + X2 = 446 + 3164.0625 Reorder the terms: 3164.0625 + 112.5X + X2 = 446 + 3164.0625 Combine like terms: 446 + 3164.0625 = 3610.0625 3164.0625 + 112.5X + X2 = 3610.0625 Factor a perfect square on the left side: (X + 56.25)(X + 56.25) = 3610.0625 Calculate the square root of the right side: 60.083795652 Break this problem into two subproblems by setting (X + 56.25) equal to 60.083795652 and -60.083795652.Subproblem 1
X + 56.25 = 60.083795652 Simplifying X + 56.25 = 60.083795652 Reorder the terms: 56.25 + X = 60.083795652 Solving 56.25 + X = 60.083795652 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-56.25' to each side of the equation. 56.25 + -56.25 + X = 60.083795652 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + X = 60.083795652 + -56.25 X = 60.083795652 + -56.25 Combine like terms: 60.083795652 + -56.25 = 3.833795652 X = 3.833795652 Simplifying X = 3.833795652Subproblem 2
X + 56.25 = -60.083795652 Simplifying X + 56.25 = -60.083795652 Reorder the terms: 56.25 + X = -60.083795652 Solving 56.25 + X = -60.083795652 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-56.25' to each side of the equation. 56.25 + -56.25 + X = -60.083795652 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + X = -60.083795652 + -56.25 X = -60.083795652 + -56.25 Combine like terms: -60.083795652 + -56.25 = -116.333795652 X = -116.333795652 Simplifying X = -116.333795652Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.833795652, -116.333795652}
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