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Simplifying 4x2 + 20x + 41 = 0 Reorder the terms: 41 + 20x + 4x2 = 0 Solving 41 + 20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10.25 + 5x + x2 = 0 Move the constant term to the right: Add '-10.25' to each side of the equation. 10.25 + 5x + -10.25 + x2 = 0 + -10.25 Reorder the terms: 10.25 + -10.25 + 5x + x2 = 0 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + 5x + x2 = 0 + -10.25 5x + x2 = 0 + -10.25 Combine like terms: 0 + -10.25 = -10.25 5x + x2 = -10.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -10.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -10.25 + 6.25 Combine like terms: -10.25 + 6.25 = -4 6.25 + 5x + x2 = -4 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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