k^2+22k+35=0

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Solution for k^2+22k+35=0 equation: 


Simplifying
k2 + 22k + 35 = 0

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

Solving
35 + 22k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 22k + -35 + k2 = 0 + -35

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

Combine like terms: 35 + -35 = 0
0 + 22k + k2 = 0 + -35
22k + k2 = 0 + -35

Combine like terms: 0 + -35 = -35
22k + k2 = -35

The k term is 22k.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22k + 121 + k2 = -35 + 121

Reorder the terms:
121 + 22k + k2 = -35 + 121

Combine like terms: -35 + 121 = 86
121 + 22k + k2 = 86

Factor a perfect square on the left side:
(k + 11)(k + 11) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(k + 11) equal to 9.273618495 and -9.273618495.


Subproblem 1
k + 11 = 9.273618495

Simplifying
k + 11 = 9.273618495

Reorder the terms:
11 + k = 9.273618495

Solving
11 + k = 9.273618495

Solving for variable 'k'.

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

Add '-11' to each side of the equation.
11 + -11 + k = 9.273618495 + -11

Combine like terms: 11 + -11 = 0
0 + k = 9.273618495 + -11
k = 9.273618495 + -11

Combine like terms: 9.273618495 + -11 = -1.726381505
k = -1.726381505

Simplifying
k = -1.726381505


Subproblem 2
k + 11 = -9.273618495

Simplifying
k + 11 = -9.273618495

Reorder the terms:
11 + k = -9.273618495

Solving
11 + k = -9.273618495

Solving for variable 'k'.

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

Add '-11' to each side of the equation.
11 + -11 + k = -9.273618495 + -11

Combine like terms: 11 + -11 = 0
0 + k = -9.273618495 + -11
k = -9.273618495 + -11

Combine like terms: -9.273618495 + -11 = -20.273618495
k = -20.273618495

Simplifying
k = -20.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-1.726381505, -20.273618495}

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