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Simplifying w2 + 9 = 2w2 + -2w + 21 Reorder the terms: 9 + w2 = 2w2 + -2w + 21 Reorder the terms: 9 + w2 = 21 + -2w + 2w2 Solving 9 + w2 = 21 + -2w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + -21 + 2w + w2 + -2w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Combine like terms: 9 + -21 = -12 -12 + 2w + w2 + -2w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -12 + 2w + -1w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Reorder the terms: -12 + 2w + -1w2 = 21 + -21 + -2w + 2w + 2w2 + -2w2 Combine like terms: 21 + -21 = 0 -12 + 2w + -1w2 = 0 + -2w + 2w + 2w2 + -2w2 -12 + 2w + -1w2 = -2w + 2w + 2w2 + -2w2 Combine like terms: -2w + 2w = 0 -12 + 2w + -1w2 = 0 + 2w2 + -2w2 -12 + 2w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -12 + 2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -2w + w2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -2w + -12 + w2 = 0 + -12 Reorder the terms: 12 + -12 + -2w + w2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2w + w2 = 0 + -12 -2w + w2 = 0 + -12 Combine like terms: 0 + -12 = -12 -2w + w2 = -12 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = -12 + 1 Reorder the terms: 1 + -2w + w2 = -12 + 1 Combine like terms: -12 + 1 = -11 1 + -2w + w2 = -11 Factor a perfect square on the left side: (w + -1)(w + -1) = -11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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