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Simplifying (3k + -5) = (2k2 + 4k + -3) Reorder the terms: (-5 + 3k) = (2k2 + 4k + -3) Remove parenthesis around (-5 + 3k) -5 + 3k = (2k2 + 4k + -3) Reorder the terms: -5 + 3k = (-3 + 4k + 2k2) Remove parenthesis around (-3 + 4k + 2k2) -5 + 3k = -3 + 4k + 2k2 Solving -5 + 3k = -3 + 4k + 2k2 Solving for variable 'k'. Reorder the terms: -5 + 3 + 3k + -4k + -2k2 = -3 + 4k + 2k2 + 3 + -4k + -2k2 Combine like terms: -5 + 3 = -2 -2 + 3k + -4k + -2k2 = -3 + 4k + 2k2 + 3 + -4k + -2k2 Combine like terms: 3k + -4k = -1k -2 + -1k + -2k2 = -3 + 4k + 2k2 + 3 + -4k + -2k2 Reorder the terms: -2 + -1k + -2k2 = -3 + 3 + 4k + -4k + 2k2 + -2k2 Combine like terms: -3 + 3 = 0 -2 + -1k + -2k2 = 0 + 4k + -4k + 2k2 + -2k2 -2 + -1k + -2k2 = 4k + -4k + 2k2 + -2k2 Combine like terms: 4k + -4k = 0 -2 + -1k + -2k2 = 0 + 2k2 + -2k2 -2 + -1k + -2k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -2 + -1k + -2k2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + k + 2k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + k + 2k2)' equal to zero and attempt to solve: Simplifying 2 + k + 2k2 = 0 Solving 2 + k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 0.5k + k2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.5k + -1 + k2 = 0 + -1 Reorder the terms: 1 + -1 + 0.5k + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.5k + k2 = 0 + -1 0.5k + k2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.5k + k2 = -1 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5k + 0.25 + k2 = -1 + 0.25 Reorder the terms: 0.25 + 0.5k + k2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.5k + k2 = -0.75 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -0.75 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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