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Simplifying X2 + 2X + -200 = 0 Reorder the terms: -200 + 2X + X2 = 0 Solving -200 + 2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 2X + 200 + X2 = 0 + 200 Reorder the terms: -200 + 200 + 2X + X2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 2X + X2 = 0 + 200 2X + X2 = 0 + 200 Combine like terms: 0 + 200 = 200 2X + X2 = 200 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 200 + 1 Reorder the terms: 1 + 2X + X2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + 2X + X2 = 201 Factor a perfect square on the left side: (X + 1)(X + 1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (X + 1) equal to 14.177446879 and -14.177446879.Subproblem 1
X + 1 = 14.177446879 Simplifying X + 1 = 14.177446879 Reorder the terms: 1 + X = 14.177446879 Solving 1 + X = 14.177446879 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + X = 14.177446879 + -1 X = 14.177446879 + -1 Combine like terms: 14.177446879 + -1 = 13.177446879 X = 13.177446879 Simplifying X = 13.177446879Subproblem 2
X + 1 = -14.177446879 Simplifying X + 1 = -14.177446879 Reorder the terms: 1 + X = -14.177446879 Solving 1 + X = -14.177446879 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + X = -14.177446879 + -1 X = -14.177446879 + -1 Combine like terms: -14.177446879 + -1 = -15.177446879 X = -15.177446879 Simplifying X = -15.177446879Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.177446879, -15.177446879}
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