36+16x+x^2=0

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


Simplifying
36 + 16x + x2 = 0

Solving
36 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 16x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 16x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 16x + x2 = 0 + -36
16x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
16x + x2 = -36

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

Add '64' to each side of the equation.
16x + 64 + x2 = -36 + 64

Reorder the terms:
64 + 16x + x2 = -36 + 64

Combine like terms: -36 + 64 = 28
64 + 16x + x2 = 28

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

Calculate the square root of the right side: 5.291502622

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


Subproblem 1
x + 8 = 5.291502622

Simplifying
x + 8 = 5.291502622

Reorder the terms:
8 + x = 5.291502622

Solving
8 + x = 5.291502622

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 5.291502622 + -8

Combine like terms: 8 + -8 = 0
0 + x = 5.291502622 + -8
x = 5.291502622 + -8

Combine like terms: 5.291502622 + -8 = -2.708497378
x = -2.708497378

Simplifying
x = -2.708497378


Subproblem 2
x + 8 = -5.291502622

Simplifying
x + 8 = -5.291502622

Reorder the terms:
8 + x = -5.291502622

Solving
8 + x = -5.291502622

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -5.291502622 + -8

Combine like terms: 8 + -8 = 0
0 + x = -5.291502622 + -8
x = -5.291502622 + -8

Combine like terms: -5.291502622 + -8 = -13.291502622
x = -13.291502622

Simplifying
x = -13.291502622


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

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