4k^2=6k-4

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Solution for 4k^2=6k-4 equation:


Simplifying
4k2 = 6k + -4

Reorder the terms:
4k2 = -4 + 6k

Solving
4k2 = -4 + 6k

Solving for variable 'k'.

Reorder the terms:
4 + -6k + 4k2 = -4 + 6k + 4 + -6k

Reorder the terms:
4 + -6k + 4k2 = -4 + 4 + 6k + -6k

Combine like terms: -4 + 4 = 0
4 + -6k + 4k2 = 0 + 6k + -6k
4 + -6k + 4k2 = 6k + -6k

Combine like terms: 6k + -6k = 0
4 + -6k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3k + 2k2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -3k + 2k2)' equal to zero and attempt to solve: Simplifying 2 + -3k + 2k2 = 0 Solving 2 + -3k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -1.5k + k2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.5k + -1 + k2 = 0 + -1 Reorder the terms: 1 + -1 + -1.5k + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.5k + k2 = 0 + -1 -1.5k + k2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.5k + k2 = -1 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 = -1 + 0.5625 Reorder the terms: 0.5625 + -1.5k + k2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + -1.5k + k2 = -0.4375 Factor a perfect square on the left side: (k + -0.75)(k + -0.75) = -0.4375 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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