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Simplifying (-3w2 + 6w + -5) + (-8w2 + 7w + 7) + -1(-5w2 + 6w + 8) = 0 Reorder the terms: (-5 + 6w + -3w2) + (-8w2 + 7w + 7) + -1(-5w2 + 6w + 8) = 0 Remove parenthesis around (-5 + 6w + -3w2) -5 + 6w + -3w2 + (-8w2 + 7w + 7) + -1(-5w2 + 6w + 8) = 0 Reorder the terms: -5 + 6w + -3w2 + (7 + 7w + -8w2) + -1(-5w2 + 6w + 8) = 0 Remove parenthesis around (7 + 7w + -8w2) -5 + 6w + -3w2 + 7 + 7w + -8w2 + -1(-5w2 + 6w + 8) = 0 Reorder the terms: -5 + 6w + -3w2 + 7 + 7w + -8w2 + -1(8 + 6w + -5w2) = 0 -5 + 6w + -3w2 + 7 + 7w + -8w2 + (8 * -1 + 6w * -1 + -5w2 * -1) = 0 -5 + 6w + -3w2 + 7 + 7w + -8w2 + (-8 + -6w + 5w2) = 0 Reorder the terms: -5 + 7 + -8 + 6w + 7w + -6w + -3w2 + -8w2 + 5w2 = 0 Combine like terms: -5 + 7 = 2 2 + -8 + 6w + 7w + -6w + -3w2 + -8w2 + 5w2 = 0 Combine like terms: 2 + -8 = -6 -6 + 6w + 7w + -6w + -3w2 + -8w2 + 5w2 = 0 Combine like terms: 6w + 7w = 13w -6 + 13w + -6w + -3w2 + -8w2 + 5w2 = 0 Combine like terms: 13w + -6w = 7w -6 + 7w + -3w2 + -8w2 + 5w2 = 0 Combine like terms: -3w2 + -8w2 = -11w2 -6 + 7w + -11w2 + 5w2 = 0 Combine like terms: -11w2 + 5w2 = -6w2 -6 + 7w + -6w2 = 0 Solving -6 + 7w + -6w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 1 + -1.166666667w + w2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.166666667w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -1.166666667w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.166666667w + w2 = 0 + -1 -1.166666667w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.166666667w + w2 = -1 The w term is -1.166666667w. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667w + 0.3402777780 + w2 = -1 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667w + w2 = -1 + 0.3402777780 Combine like terms: -1 + 0.3402777780 = -0.659722222 0.3402777780 + -1.166666667w + w2 = -0.659722222 Factor a perfect square on the left side: (w + -0.5833333335)(w + -0.5833333335) = -0.659722222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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