(x^2)+(x+1)=113

Solution for (x^2)+(x+1)=113 equation:

Simplifying
(x2) + (x + 1) = 113
x2 + (x + 1) = 113

Reorder the terms:
x2 + (1 + x) = 113

Remove parenthesis around (1 + x)
x2 + 1 + x = 113

Reorder the terms:
1 + x + x2 = 113

Solving
1 + x + x2 = 113

Solving for variable 'x'.

Reorder the terms:
1 + -113 + x + x2 = 113 + -113

Combine like terms: 1 + -113 = -112
-112 + x + x2 = 113 + -113

Combine like terms: 113 + -113 = 0
-112 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + x + x2 = 0 + 112
x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
x + x2 = 112

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 112 + 0.25

Reorder the terms:
0.25 + x + x2 = 112 + 0.25

Combine like terms: 112 + 0.25 = 112.25
0.25 + x + x2 = 112.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.59481005 and -10.59481005.

Subproblem 1
x + 0.5 = 10.59481005

Simplifying
x + 0.5 = 10.59481005

Reorder the terms:
0.5 + x = 10.59481005

Solving
0.5 + x = 10.59481005

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 10.59481005 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 10.59481005 + -0.5
x = 10.59481005 + -0.5

Combine like terms: 10.59481005 + -0.5 = 10.09481005
x = 10.09481005

Simplifying
x = 10.09481005

Subproblem 2
x + 0.5 = -10.59481005

Simplifying
x + 0.5 = -10.59481005

Reorder the terms:
0.5 + x = -10.59481005

Solving
0.5 + x = -10.59481005

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -10.59481005 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -10.59481005 + -0.5
x = -10.59481005 + -0.5

Combine like terms: -10.59481005 + -0.5 = -11.09481005
x = -11.09481005

Simplifying
x = -11.09481005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.09481005, -11.09481005}