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Simplifying 4w2 + 21w + 32 = 0 Reorder the terms: 32 + 21w + 4w2 = 0 Solving 32 + 21w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8 + 5.25w + w2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 5.25w + -8 + w2 = 0 + -8 Reorder the terms: 8 + -8 + 5.25w + w2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5.25w + w2 = 0 + -8 5.25w + w2 = 0 + -8 Combine like terms: 0 + -8 = -8 5.25w + w2 = -8 The w term is 5.25w. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25w + 6.890625 + w2 = -8 + 6.890625 Reorder the terms: 6.890625 + 5.25w + w2 = -8 + 6.890625 Combine like terms: -8 + 6.890625 = -1.109375 6.890625 + 5.25w + w2 = -1.109375 Factor a perfect square on the left side: (w + 2.625)(w + 2.625) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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