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Simplifying 77 = (10 + -3w) * w Reorder the terms for easier multiplication: 77 = w(10 + -3w) 77 = (10 * w + -3w * w) 77 = (10w + -3w2) Solving 77 = 10w + -3w2 Solving for variable 'w'. Reorder the terms: 77 + -10w + 3w2 = 10w + -10w + -3w2 + 3w2 Combine like terms: 10w + -10w = 0 77 + -10w + 3w2 = 0 + -3w2 + 3w2 77 + -10w + 3w2 = -3w2 + 3w2 Combine like terms: -3w2 + 3w2 = 0 77 + -10w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 25.66666667 + -3.333333333w + w2 = 0 Move the constant term to the right: Add '-25.66666667' to each side of the equation. 25.66666667 + -3.333333333w + -25.66666667 + w2 = 0 + -25.66666667 Reorder the terms: 25.66666667 + -25.66666667 + -3.333333333w + w2 = 0 + -25.66666667 Combine like terms: 25.66666667 + -25.66666667 = 0.00000000 0.00000000 + -3.333333333w + w2 = 0 + -25.66666667 -3.333333333w + w2 = 0 + -25.66666667 Combine like terms: 0 + -25.66666667 = -25.66666667 -3.333333333w + w2 = -25.66666667 The w term is -3.333333333w. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333w + 2.777777779 + w2 = -25.66666667 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333w + w2 = -25.66666667 + 2.777777779 Combine like terms: -25.66666667 + 2.777777779 = -22.888888891 2.777777779 + -3.333333333w + w2 = -22.888888891 Factor a perfect square on the left side: (w + -1.666666667)(w + -1.666666667) = -22.888888891 Can't calculate square root of the right side. The solution to this equation could not be determined.
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