14k^2-189k+91=0

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Solution for 14k^2-189k+91=0 equation:


Simplifying
14k2 + -189k + 91 = 0

Reorder the terms:
91 + -189k + 14k2 = 0

Solving
91 + -189k + 14k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(13 + -27k + 2k2) = 0

Factor a trinomial.
7((1 + -2k)(13 + -1k)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(1 + -2k)' equal to zero and attempt to solve: Simplifying 1 + -2k = 0 Solving 1 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k = 0 + -1 -2k = 0 + -1 Combine like terms: 0 + -1 = -1 -2k = -1 Divide each side by '-2'. k = 0.5 Simplifying k = 0.5

Subproblem 2

Set the factor '(13 + -1k)' equal to zero and attempt to solve: Simplifying 13 + -1k = 0 Solving 13 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1k = 0 + -13 -1k = 0 + -13 Combine like terms: 0 + -13 = -13 -1k = -13 Divide each side by '-1'. k = 13 Simplifying k = 13

Solution

k = {0.5, 13}

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