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Simplifying x2 + -0.2x + -0.01 = 0 Reorder the terms: -0.01 + -0.2x + x2 = 0 Solving -0.01 + -0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + -0.2x + 0.01 + x2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + -0.2x + x2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + -0.2x + x2 = 0 + 0.01 -0.2x + x2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 -0.2x + x2 = 0.01 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 = 0.01 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.01 + 0.01 Combine like terms: 0.01 + 0.01 = 0.02 0.01 + -0.2x + x2 = 0.02 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.02 Calculate the square root of the right side: 0.141421356 Break this problem into two subproblems by setting (x + -0.1) equal to 0.141421356 and -0.141421356.Subproblem 1
x + -0.1 = 0.141421356 Simplifying x + -0.1 = 0.141421356 Reorder the terms: -0.1 + x = 0.141421356 Solving -0.1 + x = 0.141421356 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 = 0.141421356 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.141421356 + 0.1 x = 0.141421356 + 0.1 Combine like terms: 0.141421356 + 0.1 = 0.241421356 x = 0.241421356 Simplifying x = 0.241421356Subproblem 2
x + -0.1 = -0.141421356 Simplifying x + -0.1 = -0.141421356 Reorder the terms: -0.1 + x = -0.141421356 Solving -0.1 + x = -0.141421356 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 = -0.141421356 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.141421356 + 0.1 x = -0.141421356 + 0.1 Combine like terms: -0.141421356 + 0.1 = -0.041421356 x = -0.041421356 Simplifying x = -0.041421356Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.241421356, -0.041421356}
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