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Simplifying 4w2 = 10w + -13 Reorder the terms: 4w2 = -13 + 10w Solving 4w2 = -13 + 10w Solving for variable 'w'. Reorder the terms: 13 + -10w + 4w2 = -13 + 10w + 13 + -10w Reorder the terms: 13 + -10w + 4w2 = -13 + 13 + 10w + -10w Combine like terms: -13 + 13 = 0 13 + -10w + 4w2 = 0 + 10w + -10w 13 + -10w + 4w2 = 10w + -10w Combine like terms: 10w + -10w = 0 13 + -10w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -2.5w + w2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -2.5w + -3.25 + w2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -2.5w + w2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -2.5w + w2 = 0 + -3.25 -2.5w + w2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -2.5w + w2 = -3.25 The w term is -2.5w. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5w + 1.5625 + w2 = -3.25 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = -3.25 + 1.5625 Combine like terms: -3.25 + 1.5625 = -1.6875 1.5625 + -2.5w + w2 = -1.6875 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = -1.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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