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Simplifying 0 = k2 + -10k + 61 Reorder the terms: 0 = 61 + -10k + k2 Solving 0 = 61 + -10k + k2 Solving for variable 'k'. Combine like terms: 0 + -61 = -61 -61 + 10k + -1k2 = 61 + -10k + k2 + -61 + 10k + -1k2 Reorder the terms: -61 + 10k + -1k2 = 61 + -61 + -10k + 10k + k2 + -1k2 Combine like terms: 61 + -61 = 0 -61 + 10k + -1k2 = 0 + -10k + 10k + k2 + -1k2 -61 + 10k + -1k2 = -10k + 10k + k2 + -1k2 Combine like terms: -10k + 10k = 0 -61 + 10k + -1k2 = 0 + k2 + -1k2 -61 + 10k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -61 + 10k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 61 + -10k + k2 = 0 Move the constant term to the right: Add '-61' to each side of the equation. 61 + -10k + -61 + k2 = 0 + -61 Reorder the terms: 61 + -61 + -10k + k2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + -10k + k2 = 0 + -61 -10k + k2 = 0 + -61 Combine like terms: 0 + -61 = -61 -10k + k2 = -61 The k term is -10k. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10k + 25 + k2 = -61 + 25 Reorder the terms: 25 + -10k + k2 = -61 + 25 Combine like terms: -61 + 25 = -36 25 + -10k + k2 = -36 Factor a perfect square on the left side: (k + -5)(k + -5) = -36 Can't calculate square root of the right side. The solution to this equation could not be determined.
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