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Simplifying 6(5k + -8) + -20 = 11k(2k + -3) + 3k Reorder the terms: 6(-8 + 5k) + -20 = 11k(2k + -3) + 3k (-8 * 6 + 5k * 6) + -20 = 11k(2k + -3) + 3k (-48 + 30k) + -20 = 11k(2k + -3) + 3k Reorder the terms: -48 + -20 + 30k = 11k(2k + -3) + 3k Combine like terms: -48 + -20 = -68 -68 + 30k = 11k(2k + -3) + 3k Reorder the terms: -68 + 30k = 11k(-3 + 2k) + 3k -68 + 30k = (-3 * 11k + 2k * 11k) + 3k -68 + 30k = (-33k + 22k2) + 3k Reorder the terms: -68 + 30k = -33k + 3k + 22k2 Combine like terms: -33k + 3k = -30k -68 + 30k = -30k + 22k2 Solving -68 + 30k = -30k + 22k2 Solving for variable 'k'. Combine like terms: 30k + 30k = 60k -68 + 60k + -22k2 = -30k + 22k2 + 30k + -22k2 Reorder the terms: -68 + 60k + -22k2 = -30k + 30k + 22k2 + -22k2 Combine like terms: -30k + 30k = 0 -68 + 60k + -22k2 = 0 + 22k2 + -22k2 -68 + 60k + -22k2 = 22k2 + -22k2 Combine like terms: 22k2 + -22k2 = 0 -68 + 60k + -22k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-34 + 30k + -11k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-34 + 30k + -11k2)' equal to zero and attempt to solve: Simplifying -34 + 30k + -11k2 = 0 Solving -34 + 30k + -11k2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. 3.090909091 + -2.727272727k + k2 = 0 Move the constant term to the right: Add '-3.090909091' to each side of the equation. 3.090909091 + -2.727272727k + -3.090909091 + k2 = 0 + -3.090909091 Reorder the terms: 3.090909091 + -3.090909091 + -2.727272727k + k2 = 0 + -3.090909091 Combine like terms: 3.090909091 + -3.090909091 = 0.000000000 0.000000000 + -2.727272727k + k2 = 0 + -3.090909091 -2.727272727k + k2 = 0 + -3.090909091 Combine like terms: 0 + -3.090909091 = -3.090909091 -2.727272727k + k2 = -3.090909091 The k term is -2.727272727k. Take half its coefficient (-1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. -2.727272727k + 1.859504133 + k2 = -3.090909091 + 1.859504133 Reorder the terms: 1.859504133 + -2.727272727k + k2 = -3.090909091 + 1.859504133 Combine like terms: -3.090909091 + 1.859504133 = -1.231404958 1.859504133 + -2.727272727k + k2 = -1.231404958 Factor a perfect square on the left side: (k + -1.363636364)(k + -1.363636364) = -1.231404958 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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