35k^2-22k-11=0

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Solution for 35k^2-22k-11=0 equation: 


Simplifying
35k2 + -22k + -11 = 0

Reorder the terms:
-11 + -22k + 35k2 = 0

Solving
-11 + -22k + 35k2 = 0

Solving for variable 'k'.

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

Divide each side by '35'.
-0.3142857143 + -0.6285714286k + k2 = 0

Move the constant term to the right:

Add '0.3142857143' to each side of the equation.
-0.3142857143 + -0.6285714286k + 0.3142857143 + k2 = 0 + 0.3142857143

Reorder the terms:
-0.3142857143 + 0.3142857143 + -0.6285714286k + k2 = 0 + 0.3142857143

Combine like terms: -0.3142857143 + 0.3142857143 = 0.0000000000
0.0000000000 + -0.6285714286k + k2 = 0 + 0.3142857143
-0.6285714286k + k2 = 0 + 0.3142857143

Combine like terms: 0 + 0.3142857143 = 0.3142857143
-0.6285714286k + k2 = 0.3142857143

The k term is -0.6285714286k.  Take half its coefficient (-0.3142857143).
Square it (0.09877551021) and add it to both sides.

Add '0.09877551021' to each side of the equation.
-0.6285714286k + 0.09877551021 + k2 = 0.3142857143 + 0.09877551021

Reorder the terms:
0.09877551021 + -0.6285714286k + k2 = 0.3142857143 + 0.09877551021

Combine like terms: 0.3142857143 + 0.09877551021 = 0.41306122451
0.09877551021 + -0.6285714286k + k2 = 0.41306122451

Factor a perfect square on the left side:
(k + -0.3142857143)(k + -0.3142857143) = 0.41306122451

Calculate the square root of the right side: 0.642698393

Break this problem into two subproblems by setting 
(k + -0.3142857143) equal to 0.642698393 and -0.642698393.


Subproblem 1
k + -0.3142857143 = 0.642698393

Simplifying
k + -0.3142857143 = 0.642698393

Reorder the terms:
-0.3142857143 + k = 0.642698393

Solving
-0.3142857143 + k = 0.642698393

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '0.3142857143' to each side of the equation.
-0.3142857143 + 0.3142857143 + k = 0.642698393 + 0.3142857143

Combine like terms: -0.3142857143 + 0.3142857143 = 0.0000000000
0.0000000000 + k = 0.642698393 + 0.3142857143
k = 0.642698393 + 0.3142857143

Combine like terms: 0.642698393 + 0.3142857143 = 0.9569841073
k = 0.9569841073

Simplifying
k = 0.9569841073


Subproblem 2
k + -0.3142857143 = -0.642698393

Simplifying
k + -0.3142857143 = -0.642698393

Reorder the terms:
-0.3142857143 + k = -0.642698393

Solving
-0.3142857143 + k = -0.642698393

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '0.3142857143' to each side of the equation.
-0.3142857143 + 0.3142857143 + k = -0.642698393 + 0.3142857143

Combine like terms: -0.3142857143 + 0.3142857143 = 0.0000000000
0.0000000000 + k = -0.642698393 + 0.3142857143
k = -0.642698393 + 0.3142857143

Combine like terms: -0.642698393 + 0.3142857143 = -0.3284126787
k = -0.3284126787

Simplifying
k = -0.3284126787


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.9569841073, -0.3284126787}

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