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Simplifying 4(w + 3) * w = -15 Reorder the terms: 4(3 + w) * w = -15 Reorder the terms for easier multiplication: 4w(3 + w) = -15 (3 * 4w + w * 4w) = -15 (12w + 4w2) = -15 Solving 12w + 4w2 = -15 Solving for variable 'w'. Reorder the terms: 15 + 12w + 4w2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 12w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 3w + w2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 3w + -3.75 + w2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 3w + w2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 3w + w2 = 0 + -3.75 3w + w2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 3w + w2 = -3.75 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = -3.75 + 2.25 Reorder the terms: 2.25 + 3w + w2 = -3.75 + 2.25 Combine like terms: -3.75 + 2.25 = -1.5 2.25 + 3w + w2 = -1.5 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = -1.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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