x^2+x=25.7

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Solution for x^2+x=25.7 equation: 


Simplifying
x2 + x = 25.7

Reorder the terms:
x + x2 = 25.7

Solving
x + x2 = 25.7

Solving for variable 'x'.

Reorder the terms:
-25.7 + x + x2 = 25.7 + -25.7

Combine like terms: 25.7 + -25.7 = 0.0
-25.7 + x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '25.7' to each side of the equation.
-25.7 + x + 25.7 + x2 = 0.0 + 25.7

Reorder the terms:
-25.7 + 25.7 + x + x2 = 0.0 + 25.7

Combine like terms: -25.7 + 25.7 = 0.0
0.0 + x + x2 = 0.0 + 25.7
x + x2 = 0.0 + 25.7

Combine like terms: 0.0 + 25.7 = 25.7
x + x2 = 25.7

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 = 25.7 + 0.25

Reorder the terms:
0.25 + x + x2 = 25.7 + 0.25

Combine like terms: 25.7 + 0.25 = 25.95
0.25 + x + x2 = 25.95

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 25.95

Calculate the square root of the right side: 5.094114251

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.094114251 and -5.094114251.


Subproblem 1
x + 0.5 = 5.094114251

Simplifying
x + 0.5 = 5.094114251

Reorder the terms:
0.5 + x = 5.094114251

Solving
0.5 + x = 5.094114251

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 = 5.094114251 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.094114251 + -0.5
x = 5.094114251 + -0.5

Combine like terms: 5.094114251 + -0.5 = 4.594114251
x = 4.594114251

Simplifying
x = 4.594114251


Subproblem 2
x + 0.5 = -5.094114251

Simplifying
x + 0.5 = -5.094114251

Reorder the terms:
0.5 + x = -5.094114251

Solving
0.5 + x = -5.094114251

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 = -5.094114251 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.094114251 + -0.5
x = -5.094114251 + -0.5

Combine like terms: -5.094114251 + -0.5 = -5.594114251
x = -5.594114251

Simplifying
x = -5.594114251


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.594114251, -5.594114251}

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