k^2+16k+36=0

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Solution for k^2+16k+36=0 equation:


Simplifying
k2 + 16k + 36 = 0

Reorder the terms:
36 + 16k + k2 = 0

Solving
36 + 16k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 16k + -36 + k2 = 0 + -36

Reorder the terms:
36 + -36 + 16k + k2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 16k + k2 = 0 + -36
16k + k2 = 0 + -36

Combine like terms: 0 + -36 = -36
16k + k2 = -36

The k term is 16k.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16k + 64 + k2 = -36 + 64

Reorder the terms:
64 + 16k + k2 = -36 + 64

Combine like terms: -36 + 64 = 28
64 + 16k + k2 = 28

Factor a perfect square on the left side:
(k + 8)(k + 8) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(k + 8) equal to 5.291502622 and -5.291502622.

Subproblem 1

k + 8 = 5.291502622 Simplifying k + 8 = 5.291502622 Reorder the terms: 8 + k = 5.291502622 Solving 8 + k = 5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + k = 5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + k = 5.291502622 + -8 k = 5.291502622 + -8 Combine like terms: 5.291502622 + -8 = -2.708497378 k = -2.708497378 Simplifying k = -2.708497378

Subproblem 2

k + 8 = -5.291502622 Simplifying k + 8 = -5.291502622 Reorder the terms: 8 + k = -5.291502622 Solving 8 + k = -5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + k = -5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + k = -5.291502622 + -8 k = -5.291502622 + -8 Combine like terms: -5.291502622 + -8 = -13.291502622 k = -13.291502622 Simplifying k = -13.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. k = {-2.708497378, -13.291502622}

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