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Simplifying 8000 = -2w2 + 12w + -7 Reorder the terms: 8000 = -7 + 12w + -2w2 Solving 8000 = -7 + 12w + -2w2 Solving for variable 'w'. Combine like terms: 8000 + 7 = 8007 8007 + -12w + 2w2 = -7 + 12w + -2w2 + 7 + -12w + 2w2 Reorder the terms: 8007 + -12w + 2w2 = -7 + 7 + 12w + -12w + -2w2 + 2w2 Combine like terms: -7 + 7 = 0 8007 + -12w + 2w2 = 0 + 12w + -12w + -2w2 + 2w2 8007 + -12w + 2w2 = 12w + -12w + -2w2 + 2w2 Combine like terms: 12w + -12w = 0 8007 + -12w + 2w2 = 0 + -2w2 + 2w2 8007 + -12w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 8007 + -12w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4003.5 + -6w + w2 = 0 Move the constant term to the right: Add '-4003.5' to each side of the equation. 4003.5 + -6w + -4003.5 + w2 = 0 + -4003.5 Reorder the terms: 4003.5 + -4003.5 + -6w + w2 = 0 + -4003.5 Combine like terms: 4003.5 + -4003.5 = 0.0 0.0 + -6w + w2 = 0 + -4003.5 -6w + w2 = 0 + -4003.5 Combine like terms: 0 + -4003.5 = -4003.5 -6w + w2 = -4003.5 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = -4003.5 + 9 Reorder the terms: 9 + -6w + w2 = -4003.5 + 9 Combine like terms: -4003.5 + 9 = -3994.5 9 + -6w + w2 = -3994.5 Factor a perfect square on the left side: (w + -3)(w + -3) = -3994.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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