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Simplifying x(x + 1) + x + 2 = 0 Reorder the terms: x(1 + x) + x + 2 = 0 (1 * x + x * x) + x + 2 = 0 (1x + x2) + x + 2 = 0 Reorder the terms: 2 + 1x + x + x2 = 0 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 0 Solving 2 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2x + x2 = 0 + -2 2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2x + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + 2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2x + x2 = -1 Factor a perfect square on the left side: (x + 1)(x + 1) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined.
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