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Simplifying x2 + -1.414x + -1 = 0 Reorder the terms: -1 + -1.414x + x2 = 0 Solving -1 + -1.414x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.414x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.414x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.414x + x2 = 0 + 1 -1.414x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.414x + x2 = 1 The x term is -1.414x. Take half its coefficient (-0.707). Square it (0.499849) and add it to both sides. Add '0.499849' to each side of the equation. -1.414x + 0.499849 + x2 = 1 + 0.499849 Reorder the terms: 0.499849 + -1.414x + x2 = 1 + 0.499849 Combine like terms: 1 + 0.499849 = 1.499849 0.499849 + -1.414x + x2 = 1.499849 Factor a perfect square on the left side: (x + -0.707)(x + -0.707) = 1.499849 Calculate the square root of the right side: 1.224683224 Break this problem into two subproblems by setting (x + -0.707) equal to 1.224683224 and -1.224683224.Subproblem 1
x + -0.707 = 1.224683224 Simplifying x + -0.707 = 1.224683224 Reorder the terms: -0.707 + x = 1.224683224 Solving -0.707 + x = 1.224683224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.707' to each side of the equation. -0.707 + 0.707 + x = 1.224683224 + 0.707 Combine like terms: -0.707 + 0.707 = 0.000 0.000 + x = 1.224683224 + 0.707 x = 1.224683224 + 0.707 Combine like terms: 1.224683224 + 0.707 = 1.931683224 x = 1.931683224 Simplifying x = 1.931683224Subproblem 2
x + -0.707 = -1.224683224 Simplifying x + -0.707 = -1.224683224 Reorder the terms: -0.707 + x = -1.224683224 Solving -0.707 + x = -1.224683224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.707' to each side of the equation. -0.707 + 0.707 + x = -1.224683224 + 0.707 Combine like terms: -0.707 + 0.707 = 0.000 0.000 + x = -1.224683224 + 0.707 x = -1.224683224 + 0.707 Combine like terms: -1.224683224 + 0.707 = -0.517683224 x = -0.517683224 Simplifying x = -0.517683224Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.931683224, -0.517683224}
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