x^2+x=9.36

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Solution for x^2+x=9.36 equation: 


Simplifying
x2 + x = 9.36

Reorder the terms:
x + x2 = 9.36

Solving
x + x2 = 9.36

Solving for variable 'x'.

Reorder the terms:
-9.36 + x + x2 = 9.36 + -9.36

Combine like terms: 9.36 + -9.36 = 0.00
-9.36 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '9.36' to each side of the equation.
-9.36 + x + 9.36 + x2 = 0.00 + 9.36

Reorder the terms:
-9.36 + 9.36 + x + x2 = 0.00 + 9.36

Combine like terms: -9.36 + 9.36 = 0.00
0.00 + x + x2 = 0.00 + 9.36
x + x2 = 0.00 + 9.36

Combine like terms: 0.00 + 9.36 = 9.36
x + x2 = 9.36

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 = 9.36 + 0.25

Reorder the terms:
0.25 + x + x2 = 9.36 + 0.25

Combine like terms: 9.36 + 0.25 = 9.61
0.25 + x + x2 = 9.61

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9.61

Calculate the square root of the right side: 3.1

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.1 and -3.1.


Subproblem 1
x + 0.5 = 3.1

Simplifying
x + 0.5 = 3.1

Reorder the terms:
0.5 + x = 3.1

Solving
0.5 + x = 3.1

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 = 3.1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.1 + -0.5
x = 3.1 + -0.5

Combine like terms: 3.1 + -0.5 = 2.6
x = 2.6

Simplifying
x = 2.6


Subproblem 2
x + 0.5 = -3.1

Simplifying
x + 0.5 = -3.1

Reorder the terms:
0.5 + x = -3.1

Solving
0.5 + x = -3.1

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 = -3.1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.1 + -0.5
x = -3.1 + -0.5

Combine like terms: -3.1 + -0.5 = -3.6
x = -3.6

Simplifying
x = -3.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6, -3.6}

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