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Simplifying 4x2 + 22x + 31 = 0 Reorder the terms: 31 + 22x + 4x2 = 0 Solving 31 + 22x + 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'. 7.75 + 5.5x + x2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + 5.5x + -7.75 + x2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + 5.5x + x2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + 5.5x + x2 = 0 + -7.75 5.5x + x2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 5.5x + x2 = -7.75 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -7.75 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -7.75 + 7.5625 Combine like terms: -7.75 + 7.5625 = -0.1875 7.5625 + 5.5x + x2 = -0.1875 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -0.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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