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Simplifying 2w2 + 11w + 23 + 2w2 + 10w + 25 = 0 Reorder the terms: 23 + 25 + 11w + 10w + 2w2 + 2w2 = 0 Combine like terms: 23 + 25 = 48 48 + 11w + 10w + 2w2 + 2w2 = 0 Combine like terms: 11w + 10w = 21w 48 + 21w + 2w2 + 2w2 = 0 Combine like terms: 2w2 + 2w2 = 4w2 48 + 21w + 4w2 = 0 Solving 48 + 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'. 12 + 5.25w + w2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 5.25w + -12 + w2 = 0 + -12 Reorder the terms: 12 + -12 + 5.25w + w2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5.25w + w2 = 0 + -12 5.25w + w2 = 0 + -12 Combine like terms: 0 + -12 = -12 5.25w + w2 = -12 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 = -12 + 6.890625 Reorder the terms: 6.890625 + 5.25w + w2 = -12 + 6.890625 Combine like terms: -12 + 6.890625 = -5.109375 6.890625 + 5.25w + w2 = -5.109375 Factor a perfect square on the left side: (w + 2.625)(w + 2.625) = -5.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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