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Simplifying x2 + -2x + 0.99999 = 0 Reorder the terms: 0.99999 + -2x + x2 = 0 Solving 0.99999 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.99999' to each side of the equation. 0.99999 + -2x + -0.99999 + x2 = 0 + -0.99999 Reorder the terms: 0.99999 + -0.99999 + -2x + x2 = 0 + -0.99999 Combine like terms: 0.99999 + -0.99999 = 0.00000 0.00000 + -2x + x2 = 0 + -0.99999 -2x + x2 = 0 + -0.99999 Combine like terms: 0 + -0.99999 = -0.99999 -2x + x2 = -0.99999 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 = -0.99999 + 1 Reorder the terms: 1 + -2x + x2 = -0.99999 + 1 Combine like terms: -0.99999 + 1 = 0.00001 1 + -2x + x2 = 0.00001 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.00001 Calculate the square root of the right side: 0.003162278 Break this problem into two subproblems by setting (x + -1) equal to 0.003162278 and -0.003162278.Subproblem 1
x + -1 = 0.003162278 Simplifying x + -1 = 0.003162278 Reorder the terms: -1 + x = 0.003162278 Solving -1 + x = 0.003162278 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 = 0.003162278 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.003162278 + 1 x = 0.003162278 + 1 Combine like terms: 0.003162278 + 1 = 1.003162278 x = 1.003162278 Simplifying x = 1.003162278Subproblem 2
x + -1 = -0.003162278 Simplifying x + -1 = -0.003162278 Reorder the terms: -1 + x = -0.003162278 Solving -1 + x = -0.003162278 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 = -0.003162278 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.003162278 + 1 x = -0.003162278 + 1 Combine like terms: -0.003162278 + 1 = 0.996837722 x = 0.996837722 Simplifying x = 0.996837722Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.003162278, 0.996837722}
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