x^2+4x-5=x-6

Solution for x^2+4x-5=x-6 equation:

Simplifying
x2 + 4x + -5 = x + -6

Reorder the terms:
-5 + 4x + x2 = x + -6

Reorder the terms:
-5 + 4x + x2 = -6 + x

Solving
-5 + 4x + x2 = -6 + x

Solving for variable 'x'.

Reorder the terms:
-5 + 6 + 4x + -1x + x2 = -6 + x + 6 + -1x

Combine like terms: -5 + 6 = 1
1 + 4x + -1x + x2 = -6 + x + 6 + -1x

Combine like terms: 4x + -1x = 3x
1 + 3x + x2 = -6 + x + 6 + -1x

Reorder the terms:
1 + 3x + x2 = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
1 + 3x + x2 = 0 + x + -1x
1 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
1 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + x2 = 0 + -1
3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3x + x2 = -1

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + 3x + x2 = 1.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + 1.5 = 1.118033989

Simplifying
x + 1.5 = 1.118033989

Reorder the terms:
1.5 + x = 1.118033989

Solving
1.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.118033989 + -1.5
x = 1.118033989 + -1.5

Combine like terms: 1.118033989 + -1.5 = -0.381966011
x = -0.381966011

Simplifying
x = -0.381966011

Subproblem 2
x + 1.5 = -1.118033989

Simplifying
x + 1.5 = -1.118033989

Reorder the terms:
1.5 + x = -1.118033989

Solving
1.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.118033989 + -1.5
x = -1.118033989 + -1.5

Combine like terms: -1.118033989 + -1.5 = -2.618033989
x = -2.618033989

Simplifying
x = -2.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.381966011, -2.618033989}