k^2+2k=37

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Solution for k^2+2k=37 equation:


Simplifying
k2 + 2k = 37

Reorder the terms:
2k + k2 = 37

Solving
2k + k2 = 37

Solving for variable 'k'.

Reorder the terms:
-37 + 2k + k2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 2k + 37 + k2 = 0 + 37

Reorder the terms:
-37 + 37 + 2k + k2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 2k + k2 = 0 + 37
2k + k2 = 0 + 37

Combine like terms: 0 + 37 = 37
2k + k2 = 37

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 37 + 1

Reorder the terms:
1 + 2k + k2 = 37 + 1

Combine like terms: 37 + 1 = 38
1 + 2k + k2 = 38

Factor a perfect square on the left side:
(k + 1)(k + 1) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(k + 1) equal to 6.164414003 and -6.164414003.


Subproblem 1
k + 1 = 6.164414003

Simplifying
k + 1 = 6.164414003

Reorder the terms:
1 + k = 6.164414003

Solving
1 + k = 6.164414003

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + k = 6.164414003 + -1
k = 6.164414003 + -1

Combine like terms: 6.164414003 + -1 = 5.164414003
k = 5.164414003

Simplifying
k = 5.164414003


Subproblem 2
k + 1 = -6.164414003

Simplifying
k + 1 = -6.164414003

Reorder the terms:
1 + k = -6.164414003

Solving
1 + k = -6.164414003

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + k = -6.164414003 + -1
k = -6.164414003 + -1

Combine like terms: -6.164414003 + -1 = -7.164414003
k = -7.164414003

Simplifying
k = -7.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.164414003, -7.164414003}

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