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Simplifying 2k(2k + -1) = 4(k + -2) Reorder the terms: 2k(-1 + 2k) = 4(k + -2) (-1 * 2k + 2k * 2k) = 4(k + -2) (-2k + 4k2) = 4(k + -2) Reorder the terms: -2k + 4k2 = 4(-2 + k) -2k + 4k2 = (-2 * 4 + k * 4) -2k + 4k2 = (-8 + 4k) Solving -2k + 4k2 = -8 + 4k Solving for variable 'k'. Reorder the terms: 8 + -2k + -4k + 4k2 = -8 + 4k + 8 + -4k Combine like terms: -2k + -4k = -6k 8 + -6k + 4k2 = -8 + 4k + 8 + -4k Reorder the terms: 8 + -6k + 4k2 = -8 + 8 + 4k + -4k Combine like terms: -8 + 8 = 0 8 + -6k + 4k2 = 0 + 4k + -4k 8 + -6k + 4k2 = 4k + -4k Combine like terms: 4k + -4k = 0 8 + -6k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -3k + 2k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3k + 2k2)' equal to zero and attempt to solve: Simplifying 4 + -3k + 2k2 = 0 Solving 4 + -3k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -1.5k + k2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.5k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -1.5k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.5k + k2 = 0 + -2 -1.5k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.5k + k2 = -2 The k term is -1.5k. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5k + 0.5625 + k2 = -2 + 0.5625 Reorder the terms: 0.5625 + -1.5k + k2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + -1.5k + k2 = -1.4375 Factor a perfect square on the left side: (k + -0.75)(k + -0.75) = -1.4375 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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