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Simplifying 4w2 + 3w + 16 = 7 Reorder the terms: 16 + 3w + 4w2 = 7 Solving 16 + 3w + 4w2 = 7 Solving for variable 'w'. Reorder the terms: 16 + -7 + 3w + 4w2 = 7 + -7 Combine like terms: 16 + -7 = 9 9 + 3w + 4w2 = 7 + -7 Combine like terms: 7 + -7 = 0 9 + 3w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 0.75w + w2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 0.75w + -2.25 + w2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 0.75w + w2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 0.75w + w2 = 0 + -2.25 0.75w + w2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 0.75w + w2 = -2.25 The w term is 0.75w. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75w + 0.140625 + w2 = -2.25 + 0.140625 Reorder the terms: 0.140625 + 0.75w + w2 = -2.25 + 0.140625 Combine like terms: -2.25 + 0.140625 = -2.109375 0.140625 + 0.75w + w2 = -2.109375 Factor a perfect square on the left side: (w + 0.375)(w + 0.375) = -2.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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