18k^2-103k+119=0

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Solution for 18k^2-103k+119=0 equation:


Simplifying
18k2 + -103k + 119 = 0

Reorder the terms:
119 + -103k + 18k2 = 0

Solving
119 + -103k + 18k2 = 0

Solving for variable 'k'.

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

Divide each side by '18'.
6.611111111 + -5.722222222k + k2 = 0

Move the constant term to the right:

Add '-6.611111111' to each side of the equation.
6.611111111 + -5.722222222k + -6.611111111 + k2 = 0 + -6.611111111

Reorder the terms:
6.611111111 + -6.611111111 + -5.722222222k + k2 = 0 + -6.611111111

Combine like terms: 6.611111111 + -6.611111111 = 0.000000000
0.000000000 + -5.722222222k + k2 = 0 + -6.611111111
-5.722222222k + k2 = 0 + -6.611111111

Combine like terms: 0 + -6.611111111 = -6.611111111
-5.722222222k + k2 = -6.611111111

The k term is -5.722222222k.  Take half its coefficient (-2.861111111).
Square it (8.185956789) and add it to both sides.

Add '8.185956789' to each side of the equation.
-5.722222222k + 8.185956789 + k2 = -6.611111111 + 8.185956789

Reorder the terms:
8.185956789 + -5.722222222k + k2 = -6.611111111 + 8.185956789

Combine like terms: -6.611111111 + 8.185956789 = 1.574845678
8.185956789 + -5.722222222k + k2 = 1.574845678

Factor a perfect square on the left side:
(k + -2.861111111)(k + -2.861111111) = 1.574845678

Calculate the square root of the right side: 1.254928555

Break this problem into two subproblems by setting 
(k + -2.861111111) equal to 1.254928555 and -1.254928555.

Subproblem 1

k + -2.861111111 = 1.254928555 Simplifying k + -2.861111111 = 1.254928555 Reorder the terms: -2.861111111 + k = 1.254928555 Solving -2.861111111 + k = 1.254928555 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.861111111' to each side of the equation. -2.861111111 + 2.861111111 + k = 1.254928555 + 2.861111111 Combine like terms: -2.861111111 + 2.861111111 = 0.000000000 0.000000000 + k = 1.254928555 + 2.861111111 k = 1.254928555 + 2.861111111 Combine like terms: 1.254928555 + 2.861111111 = 4.116039666 k = 4.116039666 Simplifying k = 4.116039666

Subproblem 2

k + -2.861111111 = -1.254928555 Simplifying k + -2.861111111 = -1.254928555 Reorder the terms: -2.861111111 + k = -1.254928555 Solving -2.861111111 + k = -1.254928555 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.861111111' to each side of the equation. -2.861111111 + 2.861111111 + k = -1.254928555 + 2.861111111 Combine like terms: -2.861111111 + 2.861111111 = 0.000000000 0.000000000 + k = -1.254928555 + 2.861111111 k = -1.254928555 + 2.861111111 Combine like terms: -1.254928555 + 2.861111111 = 1.606182556 k = 1.606182556 Simplifying k = 1.606182556

Solution

The solution to the problem is based on the solutions from the subproblems. k = {4.116039666, 1.606182556}

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