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Simplifying x2 + 0.5x = 0.5 Reorder the terms: 0.5x + x2 = 0.5 Solving 0.5x + x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 0.5x + x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 0.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.5x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.5x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.5x + x2 = 0.0 + 0.5 0.5x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.5x + x2 = 0.5 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 = 0.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.5 + 0.0625 Combine like terms: 0.5 + 0.0625 = 0.5625 0.0625 + 0.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + 0.25) equal to 0.75 and -0.75.Subproblem 1
x + 0.25 = 0.75 Simplifying x + 0.25 = 0.75 Reorder the terms: 0.25 + x = 0.75 Solving 0.25 + x = 0.75 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 = 0.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.75 + -0.25 x = 0.75 + -0.25 Combine like terms: 0.75 + -0.25 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.25 = -0.75 Simplifying x + 0.25 = -0.75 Reorder the terms: 0.25 + x = -0.75 Solving 0.25 + x = -0.75 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 = -0.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.75 + -0.25 x = -0.75 + -0.25 Combine like terms: -0.75 + -0.25 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -1}
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