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Simplifying 33 + 15w = 3w + -1w * 4w Reorder the terms for easier multiplication: 33 + 15w = 3w + -1 * 4w * w Multiply -1 * 4 33 + 15w = 3w + -4w * w Multiply w * w 33 + 15w = 3w + -4w2 Solving 33 + 15w = 3w + -4w2 Solving for variable 'w'. Combine like terms: 15w + -3w = 12w 33 + 12w + 4w2 = 3w + -4w2 + -3w + 4w2 Reorder the terms: 33 + 12w + 4w2 = 3w + -3w + -4w2 + 4w2 Combine like terms: 3w + -3w = 0 33 + 12w + 4w2 = 0 + -4w2 + 4w2 33 + 12w + 4w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 33 + 12w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.25 + 3w + w2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + 3w + -8.25 + w2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + 3w + w2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + 3w + w2 = 0 + -8.25 3w + w2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 3w + w2 = -8.25 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 = -8.25 + 2.25 Reorder the terms: 2.25 + 3w + w2 = -8.25 + 2.25 Combine like terms: -8.25 + 2.25 = -6 2.25 + 3w + w2 = -6 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = -6 Can't calculate square root of the right side. The solution to this equation could not be determined.
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