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Simplifying X2 + -1X + -105 = 0 Reorder the terms: -105 + -1X + X2 = 0 Solving -105 + -1X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + -1X + 105 + X2 = 0 + 105 Reorder the terms: -105 + 105 + -1X + X2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -1X + X2 = 0 + 105 -1X + X2 = 0 + 105 Combine like terms: 0 + 105 = 105 -1X + X2 = 105 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 105 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 105 + 0.25 Combine like terms: 105 + 0.25 = 105.25 0.25 + -1X + X2 = 105.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (X + -0.5) equal to 10.259142264 and -10.259142264.Subproblem 1
X + -0.5 = 10.259142264 Simplifying X + -0.5 = 10.259142264 Reorder the terms: -0.5 + X = 10.259142264 Solving -0.5 + X = 10.259142264 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 10.259142264 + 0.5 X = 10.259142264 + 0.5 Combine like terms: 10.259142264 + 0.5 = 10.759142264 X = 10.759142264 Simplifying X = 10.759142264Subproblem 2
X + -0.5 = -10.259142264 Simplifying X + -0.5 = -10.259142264 Reorder the terms: -0.5 + X = -10.259142264 Solving -0.5 + X = -10.259142264 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -10.259142264 + 0.5 X = -10.259142264 + 0.5 Combine like terms: -10.259142264 + 0.5 = -9.759142264 X = -9.759142264 Simplifying X = -9.759142264Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.759142264, -9.759142264}
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