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Simplifying (3w2 + -1w + 4) + (5w2 + 6w + 7) = 0 Reorder the terms: (4 + -1w + 3w2) + (5w2 + 6w + 7) = 0 Remove parenthesis around (4 + -1w + 3w2) 4 + -1w + 3w2 + (5w2 + 6w + 7) = 0 Reorder the terms: 4 + -1w + 3w2 + (7 + 6w + 5w2) = 0 Remove parenthesis around (7 + 6w + 5w2) 4 + -1w + 3w2 + 7 + 6w + 5w2 = 0 Reorder the terms: 4 + 7 + -1w + 6w + 3w2 + 5w2 = 0 Combine like terms: 4 + 7 = 11 11 + -1w + 6w + 3w2 + 5w2 = 0 Combine like terms: -1w + 6w = 5w 11 + 5w + 3w2 + 5w2 = 0 Combine like terms: 3w2 + 5w2 = 8w2 11 + 5w + 8w2 = 0 Solving 11 + 5w + 8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.375 + 0.625w + w2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + 0.625w + -1.375 + w2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + 0.625w + w2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + 0.625w + w2 = 0 + -1.375 0.625w + w2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 0.625w + w2 = -1.375 The w term is 0.625w. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625w + 0.09765625 + w2 = -1.375 + 0.09765625 Reorder the terms: 0.09765625 + 0.625w + w2 = -1.375 + 0.09765625 Combine like terms: -1.375 + 0.09765625 = -1.27734375 0.09765625 + 0.625w + w2 = -1.27734375 Factor a perfect square on the left side: (w + 0.3125)(w + 0.3125) = -1.27734375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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