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Simplifying (6w2 + -3w + 1) + -1(w2 + w + -9) = 0 Reorder the terms: (1 + -3w + 6w2) + -1(w2 + w + -9) = 0 Remove parenthesis around (1 + -3w + 6w2) 1 + -3w + 6w2 + -1(w2 + w + -9) = 0 Reorder the terms: 1 + -3w + 6w2 + -1(-9 + w + w2) = 0 1 + -3w + 6w2 + (-9 * -1 + w * -1 + w2 * -1) = 0 1 + -3w + 6w2 + (9 + -1w + -1w2) = 0 Reorder the terms: 1 + 9 + -3w + -1w + 6w2 + -1w2 = 0 Combine like terms: 1 + 9 = 10 10 + -3w + -1w + 6w2 + -1w2 = 0 Combine like terms: -3w + -1w = -4w 10 + -4w + 6w2 + -1w2 = 0 Combine like terms: 6w2 + -1w2 = 5w2 10 + -4w + 5w2 = 0 Solving 10 + -4w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -0.8w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.8w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -0.8w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.8w + w2 = 0 + -2 -0.8w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.8w + w2 = -2 The w term is -0.8w. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8w + 0.16 + w2 = -2 + 0.16 Reorder the terms: 0.16 + -0.8w + w2 = -2 + 0.16 Combine like terms: -2 + 0.16 = -1.84 0.16 + -0.8w + w2 = -1.84 Factor a perfect square on the left side: (w + -0.4)(w + -0.4) = -1.84 Can't calculate square root of the right side. The solution to this equation could not be determined.
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