3k^2-18k+22=0

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Solution for 3k^2-18k+22=0 equation:


Simplifying
3k2 + -18k + 22 = 0

Reorder the terms:
22 + -18k + 3k2 = 0

Solving
22 + -18k + 3k2 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
7.333333333 + -6k + k2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + -6k + -7.333333333 + k2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + -6k + k2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + -6k + k2 = 0 + -7.333333333
-6k + k2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
-6k + k2 = -7.333333333

The k term is -6k.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6k + 9 + k2 = -7.333333333 + 9

Reorder the terms:
9 + -6k + k2 = -7.333333333 + 9

Combine like terms: -7.333333333 + 9 = 1.666666667
9 + -6k + k2 = 1.666666667

Factor a perfect square on the left side:
(k + -3)(k + -3) = 1.666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(k + -3) equal to 1.290994449 and -1.290994449.

Subproblem 1

k + -3 = 1.290994449 Simplifying k + -3 = 1.290994449 Reorder the terms: -3 + k = 1.290994449 Solving -3 + k = 1.290994449 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = 1.290994449 + 3 Combine like terms: -3 + 3 = 0 0 + k = 1.290994449 + 3 k = 1.290994449 + 3 Combine like terms: 1.290994449 + 3 = 4.290994449 k = 4.290994449 Simplifying k = 4.290994449

Subproblem 2

k + -3 = -1.290994449 Simplifying k + -3 = -1.290994449 Reorder the terms: -3 + k = -1.290994449 Solving -3 + k = -1.290994449 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = -1.290994449 + 3 Combine like terms: -3 + 3 = 0 0 + k = -1.290994449 + 3 k = -1.290994449 + 3 Combine like terms: -1.290994449 + 3 = 1.709005551 k = 1.709005551 Simplifying k = 1.709005551

Solution

The solution to the problem is based on the solutions from the subproblems. k = {4.290994449, 1.709005551}

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