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Simplifying (7w2 + -4w + -1) + (5w2 + -3w + 6) = 0 Reorder the terms: (-1 + -4w + 7w2) + (5w2 + -3w + 6) = 0 Remove parenthesis around (-1 + -4w + 7w2) -1 + -4w + 7w2 + (5w2 + -3w + 6) = 0 Reorder the terms: -1 + -4w + 7w2 + (6 + -3w + 5w2) = 0 Remove parenthesis around (6 + -3w + 5w2) -1 + -4w + 7w2 + 6 + -3w + 5w2 = 0 Reorder the terms: -1 + 6 + -4w + -3w + 7w2 + 5w2 = 0 Combine like terms: -1 + 6 = 5 5 + -4w + -3w + 7w2 + 5w2 = 0 Combine like terms: -4w + -3w = -7w 5 + -7w + 7w2 + 5w2 = 0 Combine like terms: 7w2 + 5w2 = 12w2 5 + -7w + 12w2 = 0 Solving 5 + -7w + 12w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -0.5833333333w + w2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.5833333333w + -0.4166666667 + w2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -0.5833333333w + w2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -0.5833333333w + w2 = 0 + -0.4166666667 -0.5833333333w + w2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -0.5833333333w + w2 = -0.4166666667 The w term is -0.5833333333w. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333w + 0.08506944446 + w2 = -0.4166666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333w + w2 = -0.4166666667 + 0.08506944446 Combine like terms: -0.4166666667 + 0.08506944446 = -0.33159722224 0.08506944446 + -0.5833333333w + w2 = -0.33159722224 Factor a perfect square on the left side: (w + -0.2916666667)(w + -0.2916666667) = -0.33159722224 Can't calculate square root of the right side. The solution to this equation could not be determined.
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