k^2+k=35

Solution for k^2+k=35 equation:

Simplifying
k2 + k = 35

Reorder the terms:
k + k2 = 35

Solving
k + k2 = 35

Solving for variable 'k'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
k + 0.25 + k2 = 35 + 0.25

Reorder the terms:
0.25 + k + k2 = 35 + 0.25

Combine like terms: 35 + 0.25 = 35.25
0.25 + k + k2 = 35.25

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(k + 0.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
k + 0.5 = 5.937171044

Simplifying
k + 0.5 = 5.937171044

Reorder the terms:
0.5 + k = 5.937171044

Solving
0.5 + k = 5.937171044

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = 5.937171044 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = 5.937171044 + -0.5
k = 5.937171044 + -0.5

Combine like terms: 5.937171044 + -0.5 = 5.437171044
k = 5.437171044

Simplifying
k = 5.437171044

Subproblem 2
k + 0.5 = -5.937171044

Simplifying
k + 0.5 = -5.937171044

Reorder the terms:
0.5 + k = -5.937171044

Solving
0.5 + k = -5.937171044

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = -5.937171044 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = -5.937171044 + -0.5
k = -5.937171044 + -0.5

Combine like terms: -5.937171044 + -0.5 = -6.437171044
k = -6.437171044

Simplifying
k = -6.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.437171044, -6.437171044}