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Simplifying (-1w + 8w2 + -3w) + -1(4w2 + 5w + -7) = 0 Reorder the terms: (-1w + -3w + 8w2) + -1(4w2 + 5w + -7) = 0 Combine like terms: -1w + -3w = -4w (-4w + 8w2) + -1(4w2 + 5w + -7) = 0 Remove parenthesis around (-4w + 8w2) -4w + 8w2 + -1(4w2 + 5w + -7) = 0 Reorder the terms: -4w + 8w2 + -1(-7 + 5w + 4w2) = 0 -4w + 8w2 + (-7 * -1 + 5w * -1 + 4w2 * -1) = 0 -4w + 8w2 + (7 + -5w + -4w2) = 0 Reorder the terms: 7 + -4w + -5w + 8w2 + -4w2 = 0 Combine like terms: -4w + -5w = -9w 7 + -9w + 8w2 + -4w2 = 0 Combine like terms: 8w2 + -4w2 = 4w2 7 + -9w + 4w2 = 0 Solving 7 + -9w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -2.25w + w2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -2.25w + -1.75 + w2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -2.25w + w2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -2.25w + w2 = 0 + -1.75 -2.25w + w2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -2.25w + w2 = -1.75 The w term is -2.25w. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25w + 1.265625 + w2 = -1.75 + 1.265625 Reorder the terms: 1.265625 + -2.25w + w2 = -1.75 + 1.265625 Combine like terms: -1.75 + 1.265625 = -0.484375 1.265625 + -2.25w + w2 = -0.484375 Factor a perfect square on the left side: (w + -1.125)(w + -1.125) = -0.484375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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