x^2+x-13.4=0

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Solution for x^2+x-13.4=0 equation: 


Simplifying
x2 + x + -13.4 = 0

Reorder the terms:
-13.4 + x + x2 = 0

Solving
-13.4 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13.4' to each side of the equation.
-13.4 + x + 13.4 + x2 = 0 + 13.4

Reorder the terms:
-13.4 + 13.4 + x + x2 = 0 + 13.4

Combine like terms: -13.4 + 13.4 = 0.0
0.0 + x + x2 = 0 + 13.4
x + x2 = 0 + 13.4

Combine like terms: 0 + 13.4 = 13.4
x + x2 = 13.4

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 = 13.4 + 0.25

Reorder the terms:
0.25 + x + x2 = 13.4 + 0.25

Combine like terms: 13.4 + 0.25 = 13.65
0.25 + x + x2 = 13.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.65

Calculate the square root of the right side: 3.69459064

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.69459064 and -3.69459064.


Subproblem 1
x + 0.5 = 3.69459064

Simplifying
x + 0.5 = 3.69459064

Reorder the terms:
0.5 + x = 3.69459064

Solving
0.5 + x = 3.69459064

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 = 3.69459064 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.69459064 + -0.5
x = 3.69459064 + -0.5

Combine like terms: 3.69459064 + -0.5 = 3.19459064
x = 3.19459064

Simplifying
x = 3.19459064


Subproblem 2
x + 0.5 = -3.69459064

Simplifying
x + 0.5 = -3.69459064

Reorder the terms:
0.5 + x = -3.69459064

Solving
0.5 + x = -3.69459064

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 = -3.69459064 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.69459064 + -0.5
x = -3.69459064 + -0.5

Combine like terms: -3.69459064 + -0.5 = -4.19459064
x = -4.19459064

Simplifying
x = -4.19459064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.19459064, -4.19459064}

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