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Simplifying 8x2 + 12x + 31 = 0 Reorder the terms: 31 + 12x + 8x2 = 0 Solving 31 + 12x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.875 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.875' to each side of the equation. 3.875 + 1.5x + -3.875 + x2 = 0 + -3.875 Reorder the terms: 3.875 + -3.875 + 1.5x + x2 = 0 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + 1.5x + x2 = 0 + -3.875 1.5x + x2 = 0 + -3.875 Combine like terms: 0 + -3.875 = -3.875 1.5x + x2 = -3.875 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -3.875 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.875 + 0.5625 Combine like terms: -3.875 + 0.5625 = -3.3125 0.5625 + 1.5x + x2 = -3.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -3.3125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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