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Simplifying (x + 1) + (x * x) + [(x * x) + 1] = 0 Reorder the terms: (1 + x) + (x * x) + [(x * x) + 1] = 0 Remove parenthesis around (1 + x) 1 + x + (x * x) + [(x * x) + 1] = 0 Multiply x * x 1 + x + (x2) + [(x * x) + 1] = 0 1 + x + x2 + [(x * x) + 1] = 0 Multiply x * x 1 + x + x2 + [(x2) + 1] = 0 1 + x + x2 + [x2 + 1] = 0 Reorder the terms: 1 + x + x2 + [1 + x2] = 0 Remove brackets around [1 + x2] 1 + x + x2 + 1 + x2 = 0 Reorder the terms: 1 + 1 + x + x2 + x2 = 0 Combine like terms: 1 + 1 = 2 2 + x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 2 + x + 2x2 = 0 Solving 2 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.5x + x2 = 0 + -1 0.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.5x + x2 = -1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.5x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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