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Simplifying x = 2x2 + 1 Reorder the terms: x = 1 + 2x2 Solving x = 1 + 2x2 Solving for variable 'x'. Reorder the terms: -1 + x + -2x2 = 1 + 2x2 + -1 + -2x2 Reorder the terms: -1 + x + -2x2 = 1 + -1 + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 -1 + x + -2x2 = 0 + 2x2 + -2x2 -1 + x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.5x + x2 = 0 + -0.5 -0.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.5x + x2 = -0.5 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 = -0.5 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -0.5x + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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