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Simplifying 120w2 = 3w + -7 Reorder the terms: 120w2 = -7 + 3w Solving 120w2 = -7 + 3w Solving for variable 'w'. Reorder the terms: 7 + -3w + 120w2 = -7 + 3w + 7 + -3w Reorder the terms: 7 + -3w + 120w2 = -7 + 7 + 3w + -3w Combine like terms: -7 + 7 = 0 7 + -3w + 120w2 = 0 + 3w + -3w 7 + -3w + 120w2 = 3w + -3w Combine like terms: 3w + -3w = 0 7 + -3w + 120w2 = 0 Begin completing the square. Divide all terms by 120 the coefficient of the squared term: Divide each side by '120'. 0.05833333333 + -0.025w + w2 = 0 Move the constant term to the right: Add '-0.05833333333' to each side of the equation. 0.05833333333 + -0.025w + -0.05833333333 + w2 = 0 + -0.05833333333 Reorder the terms: 0.05833333333 + -0.05833333333 + -0.025w + w2 = 0 + -0.05833333333 Combine like terms: 0.05833333333 + -0.05833333333 = 0.00000000000 0.00000000000 + -0.025w + w2 = 0 + -0.05833333333 -0.025w + w2 = 0 + -0.05833333333 Combine like terms: 0 + -0.05833333333 = -0.05833333333 -0.025w + w2 = -0.05833333333 The w term is -0.025w. Take half its coefficient (-0.0125). Square it (0.00015625) and add it to both sides. Add '0.00015625' to each side of the equation. -0.025w + 0.00015625 + w2 = -0.05833333333 + 0.00015625 Reorder the terms: 0.00015625 + -0.025w + w2 = -0.05833333333 + 0.00015625 Combine like terms: -0.05833333333 + 0.00015625 = -0.05817708333 0.00015625 + -0.025w + w2 = -0.05817708333 Factor a perfect square on the left side: (w + -0.0125)(w + -0.0125) = -0.05817708333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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