0=x^2+4x-105

Solution for 0=x^2+4x-105 equation:

Simplifying
0 = x2 + 4x + -105

Reorder the terms:
0 = -105 + 4x + x2

Solving
0 = -105 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 105 = 105
105 + -4x + -1x2 = -105 + 4x + x2 + 105 + -4x + -1x2

Reorder the terms:
105 + -4x + -1x2 = -105 + 105 + 4x + -4x + x2 + -1x2

Combine like terms: -105 + 105 = 0
105 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
105 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
105 + -4x + -1x2 = 0 + x2 + -1x2
105 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
105 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-105 + 4x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 4x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 4x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 4x + x2 = 0 + 105
4x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
4x + x2 = 105

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 105 + 4

Reorder the terms:
4 + 4x + x2 = 105 + 4

Combine like terms: 105 + 4 = 109
4 + 4x + x2 = 109

Factor a perfect square on the left side:
(x + 2)(x + 2) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(x + 2) equal to 10.440306509 and -10.440306509.

Subproblem 1
x + 2 = 10.440306509

Simplifying
x + 2 = 10.440306509

Reorder the terms:
2 + x = 10.440306509

Solving
2 + x = 10.440306509

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 10.440306509 + -2

Combine like terms: 2 + -2 = 0
0 + x = 10.440306509 + -2
x = 10.440306509 + -2

Combine like terms: 10.440306509 + -2 = 8.440306509
x = 8.440306509

Simplifying
x = 8.440306509

Subproblem 2
x + 2 = -10.440306509

Simplifying
x + 2 = -10.440306509

Reorder the terms:
2 + x = -10.440306509

Solving
2 + x = -10.440306509

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -10.440306509 + -2

Combine like terms: 2 + -2 = 0
0 + x = -10.440306509 + -2
x = -10.440306509 + -2

Combine like terms: -10.440306509 + -2 = -12.440306509
x = -12.440306509

Simplifying
x = -12.440306509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.440306509, -12.440306509}