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Simplifying (-13w2 + -25w + 32) + -1(-2w2 + -1w + -3) + (19w2 + 16w + -26) = 0 Reorder the terms: (32 + -25w + -13w2) + -1(-2w2 + -1w + -3) + (19w2 + 16w + -26) = 0 Remove parenthesis around (32 + -25w + -13w2) 32 + -25w + -13w2 + -1(-2w2 + -1w + -3) + (19w2 + 16w + -26) = 0 Reorder the terms: 32 + -25w + -13w2 + -1(-3 + -1w + -2w2) + (19w2 + 16w + -26) = 0 32 + -25w + -13w2 + (-3 * -1 + -1w * -1 + -2w2 * -1) + (19w2 + 16w + -26) = 0 32 + -25w + -13w2 + (3 + 1w + 2w2) + (19w2 + 16w + -26) = 0 Reorder the terms: 32 + -25w + -13w2 + 3 + 1w + 2w2 + (-26 + 16w + 19w2) = 0 Remove parenthesis around (-26 + 16w + 19w2) 32 + -25w + -13w2 + 3 + 1w + 2w2 + -26 + 16w + 19w2 = 0 Reorder the terms: 32 + 3 + -26 + -25w + 1w + 16w + -13w2 + 2w2 + 19w2 = 0 Combine like terms: 32 + 3 = 35 35 + -26 + -25w + 1w + 16w + -13w2 + 2w2 + 19w2 = 0 Combine like terms: 35 + -26 = 9 9 + -25w + 1w + 16w + -13w2 + 2w2 + 19w2 = 0 Combine like terms: -25w + 1w = -24w 9 + -24w + 16w + -13w2 + 2w2 + 19w2 = 0 Combine like terms: -24w + 16w = -8w 9 + -8w + -13w2 + 2w2 + 19w2 = 0 Combine like terms: -13w2 + 2w2 = -11w2 9 + -8w + -11w2 + 19w2 = 0 Combine like terms: -11w2 + 19w2 = 8w2 9 + -8w + 8w2 = 0 Solving 9 + -8w + 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'. 1.125 + -1w + w2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -1w + -1.125 + w2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -1w + w2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -1w + w2 = 0 + -1.125 -1w + w2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -1w + w2 = -1.125 The w term is -1w. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = -1.125 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -1.125 + 0.25 Combine like terms: -1.125 + 0.25 = -0.875 0.25 + -1w + w2 = -0.875 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = -0.875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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