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Simplifying (x + -0.5)(x + -0.5) = 0 Reorder the terms: (-0.5 + x)(x + -0.5) = 0 Reorder the terms: (-0.5 + x)(-0.5 + x) = 0 Multiply (-0.5 + x) * (-0.5 + x) (-0.5(-0.5 + x) + x(-0.5 + x)) = 0 ((-0.5 * -0.5 + x * -0.5) + x(-0.5 + x)) = 0 ((0.25 + -0.5x) + x(-0.5 + x)) = 0 (0.25 + -0.5x + (-0.5 * x + x * x)) = 0 (0.25 + -0.5x + (-0.5x + x2)) = 0 Combine like terms: -0.5x + -0.5x = -1x (0.25 + -1x + x2) = 0 Solving 0.25 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1x + x2 = 0 + -0.25 -1x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1x + x2 = -0.25 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 = -0.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.5) equal to 0.00 and 0.00.Subproblem 1
x + -0.5 = 0.00 Simplifying x + -0.5 = 0.00 Reorder the terms: -0.5 + x = 0.00 Solving -0.5 + x = 0.00 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 = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.00 + 0.5 x = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + -0.5 = 0.00 Simplifying x + -0.5 = 0.00 Reorder the terms: -0.5 + x = 0.00 Solving -0.5 + x = 0.00 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 = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.00 + 0.5 x = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, 0.5}
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