x=x^2+6x+5

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


Simplifying
x = x2 + 6x + 5

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

Solving
x = 5 + 6x + x2

Solving for variable 'x'.

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

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

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

Combine like terms: 5 + -5 = 0
-5 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-5 + -5x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-5 + -5x + -1x2 = 0 + x2 + -1x2
-5 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 5x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 5x + x2 = 0

Solving
5 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5x + x2 = 0 + -5
5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
5x + x2 = -5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5x + x2 = 1.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + 2.5 = 1.118033989

Simplifying
x + 2.5 = 1.118033989

Reorder the terms:
2.5 + x = 1.118033989

Solving
2.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.118033989 + -2.5
x = 1.118033989 + -2.5

Combine like terms: 1.118033989 + -2.5 = -1.381966011
x = -1.381966011

Simplifying
x = -1.381966011


Subproblem 2
x + 2.5 = -1.118033989

Simplifying
x + 2.5 = -1.118033989

Reorder the terms:
2.5 + x = -1.118033989

Solving
2.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.118033989 + -2.5
x = -1.118033989 + -2.5

Combine like terms: -1.118033989 + -2.5 = -3.618033989
x = -3.618033989

Simplifying
x = -3.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.381966011, -3.618033989}
Solution
x = {-1.381966011, -3.618033989}

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