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Simplifying 3w2 + w + 7 = 4 Reorder the terms: 7 + w + 3w2 = 4 Solving 7 + w + 3w2 = 4 Solving for variable 'w'. Reorder the terms: 7 + -4 + w + 3w2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + w + 3w2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 0.3333333333w + w2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.3333333333w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + 0.3333333333w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.3333333333w + w2 = 0 + -1 0.3333333333w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.3333333333w + w2 = -1 The w term is w. 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. 0.3333333333w + 0.25 + w2 = -1 + 0.25 Reorder the terms: 0.25 + 0.3333333333w + w2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.3333333333w + w2 = -0.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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