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Simplifying x2 + -0.25x + 0.0156 = 0 Reorder the terms: 0.0156 + -0.25x + x2 = 0 Solving 0.0156 + -0.25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0156' to each side of the equation. 0.0156 + -0.25x + -0.0156 + x2 = 0 + -0.0156 Reorder the terms: 0.0156 + -0.0156 + -0.25x + x2 = 0 + -0.0156 Combine like terms: 0.0156 + -0.0156 = 0.0000 0.0000 + -0.25x + x2 = 0 + -0.0156 -0.25x + x2 = 0 + -0.0156 Combine like terms: 0 + -0.0156 = -0.0156 -0.25x + x2 = -0.0156 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -0.0156 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -0.0156 + 0.015625 Combine like terms: -0.0156 + 0.015625 = 0.000025 0.015625 + -0.25x + x2 = 0.000025 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.000025 Calculate the square root of the right side: 0.005 Break this problem into two subproblems by setting (x + -0.125) equal to 0.005 and -0.005.Subproblem 1
x + -0.125 = 0.005 Simplifying x + -0.125 = 0.005 Reorder the terms: -0.125 + x = 0.005 Solving -0.125 + x = 0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.005 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.005 + 0.125 x = 0.005 + 0.125 Combine like terms: 0.005 + 0.125 = 0.13 x = 0.13 Simplifying x = 0.13Subproblem 2
x + -0.125 = -0.005 Simplifying x + -0.125 = -0.005 Reorder the terms: -0.125 + x = -0.005 Solving -0.125 + x = -0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.005 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.005 + 0.125 x = -0.005 + 0.125 Combine like terms: -0.005 + 0.125 = 0.12 x = 0.12 Simplifying x = 0.12Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13, 0.12}
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