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Simplifying x2 + -0.2x + 0.001 = 0 Reorder the terms: 0.001 + -0.2x + x2 = 0 Solving 0.001 + -0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.001' to each side of the equation. 0.001 + -0.2x + -0.001 + x2 = 0 + -0.001 Reorder the terms: 0.001 + -0.001 + -0.2x + x2 = 0 + -0.001 Combine like terms: 0.001 + -0.001 = 0.000 0.000 + -0.2x + x2 = 0 + -0.001 -0.2x + x2 = 0 + -0.001 Combine like terms: 0 + -0.001 = -0.001 -0.2x + x2 = -0.001 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.001 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.001 + 0.01 Combine like terms: -0.001 + 0.01 = 0.009 0.01 + -0.2x + x2 = 0.009 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.009 Calculate the square root of the right side: 0.09486833 Break this problem into two subproblems by setting (x + -0.1) equal to 0.09486833 and -0.09486833.Subproblem 1
x + -0.1 = 0.09486833 Simplifying x + -0.1 = 0.09486833 Reorder the terms: -0.1 + x = 0.09486833 Solving -0.1 + x = 0.09486833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.09486833 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.09486833 + 0.1 x = 0.09486833 + 0.1 Combine like terms: 0.09486833 + 0.1 = 0.19486833 x = 0.19486833 Simplifying x = 0.19486833Subproblem 2
x + -0.1 = -0.09486833 Simplifying x + -0.1 = -0.09486833 Reorder the terms: -0.1 + x = -0.09486833 Solving -0.1 + x = -0.09486833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.09486833 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.09486833 + 0.1 x = -0.09486833 + 0.1 Combine like terms: -0.09486833 + 0.1 = 0.00513167 x = 0.00513167 Simplifying x = 0.00513167Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19486833, 0.00513167}
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