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Simplifying X2 + 100X + -22400 = 0 Reorder the terms: -22400 + 100X + X2 = 0 Solving -22400 + 100X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '22400' to each side of the equation. -22400 + 100X + 22400 + X2 = 0 + 22400 Reorder the terms: -22400 + 22400 + 100X + X2 = 0 + 22400 Combine like terms: -22400 + 22400 = 0 0 + 100X + X2 = 0 + 22400 100X + X2 = 0 + 22400 Combine like terms: 0 + 22400 = 22400 100X + X2 = 22400 The X term is 100X. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100X + 2500 + X2 = 22400 + 2500 Reorder the terms: 2500 + 100X + X2 = 22400 + 2500 Combine like terms: 22400 + 2500 = 24900 2500 + 100X + X2 = 24900 Factor a perfect square on the left side: (X + 50)(X + 50) = 24900 Calculate the square root of the right side: 157.797338381 Break this problem into two subproblems by setting (X + 50) equal to 157.797338381 and -157.797338381.Subproblem 1
X + 50 = 157.797338381 Simplifying X + 50 = 157.797338381 Reorder the terms: 50 + X = 157.797338381 Solving 50 + X = 157.797338381 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + X = 157.797338381 + -50 Combine like terms: 50 + -50 = 0 0 + X = 157.797338381 + -50 X = 157.797338381 + -50 Combine like terms: 157.797338381 + -50 = 107.797338381 X = 107.797338381 Simplifying X = 107.797338381Subproblem 2
X + 50 = -157.797338381 Simplifying X + 50 = -157.797338381 Reorder the terms: 50 + X = -157.797338381 Solving 50 + X = -157.797338381 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + X = -157.797338381 + -50 Combine like terms: 50 + -50 = 0 0 + X = -157.797338381 + -50 X = -157.797338381 + -50 Combine like terms: -157.797338381 + -50 = -207.797338381 X = -207.797338381 Simplifying X = -207.797338381Solution
The solution to the problem is based on the solutions from the subproblems. X = {107.797338381, -207.797338381}
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