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Simplifying X2 + 0.5X + 0.0625 = 0 Reorder the terms: 0.0625 + 0.5X + X2 = 0 Solving 0.0625 + 0.5X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 0.5X + -0.0625 + X2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 0.5X + X2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 0.5X + X2 = 0 + -0.0625 0.5X + X2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 0.5X + X2 = -0.0625 The X term is 0.5X. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5X + 0.0625 + X2 = -0.0625 + 0.0625 Reorder the terms: 0.0625 + 0.5X + X2 = -0.0625 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0625 + 0.5X + X2 = 0.0000 Factor a perfect square on the left side: (X + 0.25)(X + 0.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (X + 0.25) equal to 0.0000 and 0.0000.Subproblem 1
X + 0.25 = 0.0000 Simplifying X + 0.25 = 0.0000 Reorder the terms: 0.25 + X = 0.0000 Solving 0.25 + X = 0.0000 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + X = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + X = 0.0000 + -0.25 X = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 X = -0.25 Simplifying X = -0.25Subproblem 2
X + 0.25 = 0.0000 Simplifying X + 0.25 = 0.0000 Reorder the terms: 0.25 + X = 0.0000 Solving 0.25 + X = 0.0000 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + X = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + X = 0.0000 + -0.25 X = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 X = -0.25 Simplifying X = -0.25Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.25, -0.25}
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