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Simplifying (1 + x2) * 0.35 + x = 0 Reorder the terms for easier multiplication: 0.35(1 + x2) + x = 0 (1 * 0.35 + x2 * 0.35) + x = 0 (0.35 + 0.35x2) + x = 0 Reorder the terms: 0.35 + x + 0.35x2 = 0 Solving 0.35 + x + 0.35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. 1 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.857142857x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.857142857x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.857142857x + x2 = 0 + -1 2.857142857x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.857142857x + 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. 2.857142857x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + 2.857142857x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 2.857142857x + 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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