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Simplifying x2 + -2x + 0.04 = 0 Reorder the terms: 0.04 + -2x + x2 = 0 Solving 0.04 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + -2x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + -2x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + -2x + x2 = 0 + -0.04 -2x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 -2x + x2 = -0.04 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.04 + 1 Reorder the terms: 1 + -2x + x2 = -0.04 + 1 Combine like terms: -0.04 + 1 = 0.96 1 + -2x + x2 = 0.96 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + -1) equal to 0.979795897 and -0.979795897.Subproblem 1
x + -1 = 0.979795897 Simplifying x + -1 = 0.979795897 Reorder the terms: -1 + x = 0.979795897 Solving -1 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.979795897 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.979795897 + 1 x = 0.979795897 + 1 Combine like terms: 0.979795897 + 1 = 1.979795897 x = 1.979795897 Simplifying x = 1.979795897Subproblem 2
x + -1 = -0.979795897 Simplifying x + -1 = -0.979795897 Reorder the terms: -1 + x = -0.979795897 Solving -1 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.979795897 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.979795897 + 1 x = -0.979795897 + 1 Combine like terms: -0.979795897 + 1 = 0.020204103 x = 0.020204103 Simplifying x = 0.020204103Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.979795897, 0.020204103}
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