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Simplifying 8d2 + 12d + 15 = 0 Reorder the terms: 15 + 12d + 8d2 = 0 Solving 15 + 12d + 8d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + 1.5d + d2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + 1.5d + -1.875 + d2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + 1.5d + d2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + 1.5d + d2 = 0 + -1.875 1.5d + d2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 1.5d + d2 = -1.875 The d term is 1.5d. 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. 1.5d + 0.5625 + d2 = -1.875 + 0.5625 Reorder the terms: 0.5625 + 1.5d + d2 = -1.875 + 0.5625 Combine like terms: -1.875 + 0.5625 = -1.3125 0.5625 + 1.5d + d2 = -1.3125 Factor a perfect square on the left side: (d + 0.75)(d + 0.75) = -1.3125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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