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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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