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Simplifying 4w2 = 4w + -7 Reorder the terms: 4w2 = -7 + 4w Solving 4w2 = -7 + 4w Solving for variable 'w'. Reorder the terms: 7 + -4w + 4w2 = -7 + 4w + 7 + -4w Reorder the terms: 7 + -4w + 4w2 = -7 + 7 + 4w + -4w Combine like terms: -7 + 7 = 0 7 + -4w + 4w2 = 0 + 4w + -4w 7 + -4w + 4w2 = 4w + -4w Combine like terms: 4w + -4w = 0 7 + -4w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -1w + w2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -1w + -1.75 + w2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -1w + w2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -1w + w2 = 0 + -1.75 -1w + w2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -1w + w2 = -1.75 The w term is -1w. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = -1.75 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -1.75 + 0.25 Combine like terms: -1.75 + 0.25 = -1.5 0.25 + -1w + w2 = -1.5 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = -1.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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