42.25=x^2+x

Solution for 42.25=x^2+x equation:

Simplifying
42.25 = x2 + x

Reorder the terms:
42.25 = x + x2

Solving
42.25 = x + x2

Solving for variable 'x'.

Reorder the terms:
42.25 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
42.25 + -1x + -1x2 = 0 + x2 + -1x2
42.25 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42.25 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-42.25 + x + x2 = 0

Move the constant term to the right:

Add '42.25' to each side of the equation.
-42.25 + x + 42.25 + x2 = 0 + 42.25

Reorder the terms:
-42.25 + 42.25 + x + x2 = 0 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
0.00 + x + x2 = 0 + 42.25
x + x2 = 0 + 42.25

Combine like terms: 0 + 42.25 = 42.25
x + x2 = 42.25

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.
 + 0.25 + x2 = 42.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 42.25 + 0.25

Combine like terms: 42.25 + 0.25 = 42.5
1.25 + x2 = 42.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 42.5

Calculate the square root of the right side: 6.519202405

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.519202405 and -6.519202405.

Subproblem 1
x + 0.5 = 6.519202405

Simplifying
x + 0.5 = 6.519202405

Reorder the terms:
0.5 + x = 6.519202405

Solving
0.5 + x = 6.519202405

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 = 6.519202405 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.519202405 + -0.5
x = 6.519202405 + -0.5

Combine like terms: 6.519202405 + -0.5 = 6.019202405
x = 6.019202405

Simplifying
x = 6.019202405

Subproblem 2
x + 0.5 = -6.519202405

Simplifying
x + 0.5 = -6.519202405

Reorder the terms:
0.5 + x = -6.519202405

Solving
0.5 + x = -6.519202405

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 = -6.519202405 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.519202405 + -0.5
x = -6.519202405 + -0.5

Combine like terms: -6.519202405 + -0.5 = -7.019202405
x = -7.019202405

Simplifying
x = -7.019202405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.019202405, -7.019202405}