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Simplifying (5w2 + -2w + 7) + (-3w2 + 6w + 4) = 0 Reorder the terms: (7 + -2w + 5w2) + (-3w2 + 6w + 4) = 0 Remove parenthesis around (7 + -2w + 5w2) 7 + -2w + 5w2 + (-3w2 + 6w + 4) = 0 Reorder the terms: 7 + -2w + 5w2 + (4 + 6w + -3w2) = 0 Remove parenthesis around (4 + 6w + -3w2) 7 + -2w + 5w2 + 4 + 6w + -3w2 = 0 Reorder the terms: 7 + 4 + -2w + 6w + 5w2 + -3w2 = 0 Combine like terms: 7 + 4 = 11 11 + -2w + 6w + 5w2 + -3w2 = 0 Combine like terms: -2w + 6w = 4w 11 + 4w + 5w2 + -3w2 = 0 Combine like terms: 5w2 + -3w2 = 2w2 11 + 4w + 2w2 = 0 Solving 11 + 4w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 2w + w2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 2w + -5.5 + w2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 2w + w2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 2w + w2 = 0 + -5.5 2w + w2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 2w + w2 = -5.5 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 = -5.5 + 1 Reorder the terms: 1 + 2w + w2 = -5.5 + 1 Combine like terms: -5.5 + 1 = -4.5 1 + 2w + w2 = -4.5 Factor a perfect square on the left side: (w + 1)(w + 1) = -4.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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