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Simplifying 4d4 + -20d2 + 31 = 0 Reorder the terms: 31 + -20d2 + 4d4 = 0 Solving 31 + -20d2 + 4d4 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.75 + -5d2 + d4 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + -5d2 + -7.75 + d4 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + -5d2 + d4 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + -5d2 + d4 = 0 + -7.75 -5d2 + d4 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 -5d2 + d4 = -7.75 The d term is -5d2. 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. -5d2 + 6.25 + d4 = -7.75 + 6.25 Reorder the terms: 6.25 + -5d2 + d4 = -7.75 + 6.25 Combine like terms: -7.75 + 6.25 = -1.5 6.25 + -5d2 + d4 = -1.5 Factor a perfect square on the left side: (d2 + -2.5)(d2 + -2.5) = -1.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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