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Simplifying (k2 + 2) + -1(5k2 + -5k + 7) = 0 Reorder the terms: (2 + k2) + -1(5k2 + -5k + 7) = 0 Remove parenthesis around (2 + k2) 2 + k2 + -1(5k2 + -5k + 7) = 0 Reorder the terms: 2 + k2 + -1(7 + -5k + 5k2) = 0 2 + k2 + (7 * -1 + -5k * -1 + 5k2 * -1) = 0 2 + k2 + (-7 + 5k + -5k2) = 0 Reorder the terms: 2 + -7 + 5k + k2 + -5k2 = 0 Combine like terms: 2 + -7 = -5 -5 + 5k + k2 + -5k2 = 0 Combine like terms: k2 + -5k2 = -4k2 -5 + 5k + -4k2 = 0 Solving -5 + 5k + -4k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -1.25k + k2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -1.25k + -1.25 + k2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -1.25k + k2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -1.25k + k2 = 0 + -1.25 -1.25k + k2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -1.25k + k2 = -1.25 The k term is -1.25k. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25k + 0.390625 + k2 = -1.25 + 0.390625 Reorder the terms: 0.390625 + -1.25k + k2 = -1.25 + 0.390625 Combine like terms: -1.25 + 0.390625 = -0.859375 0.390625 + -1.25k + k2 = -0.859375 Factor a perfect square on the left side: (k + -0.625)(k + -0.625) = -0.859375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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