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Simplifying 6(5k + -8) + -20 = 11(2k + -3) * 3k Reorder the terms: 6(-8 + 5k) + -20 = 11(2k + -3) * 3k (-8 * 6 + 5k * 6) + -20 = 11(2k + -3) * 3k (-48 + 30k) + -20 = 11(2k + -3) * 3k Reorder the terms: -48 + -20 + 30k = 11(2k + -3) * 3k Combine like terms: -48 + -20 = -68 -68 + 30k = 11(2k + -3) * 3k Reorder the terms: -68 + 30k = 11(-3 + 2k) * 3k Reorder the terms for easier multiplication: -68 + 30k = 11 * 3k(-3 + 2k) Multiply 11 * 3 -68 + 30k = 33k(-3 + 2k) -68 + 30k = (-3 * 33k + 2k * 33k) -68 + 30k = (-99k + 66k2) Solving -68 + 30k = -99k + 66k2 Solving for variable 'k'. Combine like terms: 30k + 99k = 129k -68 + 129k + -66k2 = -99k + 66k2 + 99k + -66k2 Reorder the terms: -68 + 129k + -66k2 = -99k + 99k + 66k2 + -66k2 Combine like terms: -99k + 99k = 0 -68 + 129k + -66k2 = 0 + 66k2 + -66k2 -68 + 129k + -66k2 = 66k2 + -66k2 Combine like terms: 66k2 + -66k2 = 0 -68 + 129k + -66k2 = 0 Begin completing the square. Divide all terms by -66 the coefficient of the squared term: Divide each side by '-66'. 1.03030303 + -1.954545455k + k2 = 0 Move the constant term to the right: Add '-1.03030303' to each side of the equation. 1.03030303 + -1.954545455k + -1.03030303 + k2 = 0 + -1.03030303 Reorder the terms: 1.03030303 + -1.03030303 + -1.954545455k + k2 = 0 + -1.03030303 Combine like terms: 1.03030303 + -1.03030303 = 0.00000000 0.00000000 + -1.954545455k + k2 = 0 + -1.03030303 -1.954545455k + k2 = 0 + -1.03030303 Combine like terms: 0 + -1.03030303 = -1.03030303 -1.954545455k + k2 = -1.03030303 The k term is -1.954545455k. Take half its coefficient (-0.9772727275). Square it (0.9550619839) and add it to both sides. Add '0.9550619839' to each side of the equation. -1.954545455k + 0.9550619839 + k2 = -1.03030303 + 0.9550619839 Reorder the terms: 0.9550619839 + -1.954545455k + k2 = -1.03030303 + 0.9550619839 Combine like terms: -1.03030303 + 0.9550619839 = -0.0752410461 0.9550619839 + -1.954545455k + k2 = -0.0752410461 Factor a perfect square on the left side: (k + -0.9772727275)(k + -0.9772727275) = -0.0752410461 Can't calculate square root of the right side. The solution to this equation could not be determined.
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