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Simplifying 5x2 + 20x + 31 = 0 Reorder the terms: 31 + 20x + 5x2 = 0 Solving 31 + 20x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.2 + 4x + x2 = 0 Move the constant term to the right: Add '-6.2' to each side of the equation. 6.2 + 4x + -6.2 + x2 = 0 + -6.2 Reorder the terms: 6.2 + -6.2 + 4x + x2 = 0 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + 4x + x2 = 0 + -6.2 4x + x2 = 0 + -6.2 Combine like terms: 0 + -6.2 = -6.2 4x + x2 = -6.2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -6.2 + 4 Reorder the terms: 4 + 4x + x2 = -6.2 + 4 Combine like terms: -6.2 + 4 = -2.2 4 + 4x + x2 = -2.2 Factor a perfect square on the left side: (x + 2)(x + 2) = -2.2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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