1.98=x^2+x

Solution for 1.98=x^2+x equation:

Simplifying
1.98 = x2 + x

Reorder the terms:
1.98 = x + x2

Solving
1.98 = x + x2

Solving for variable 'x'.

Reorder the terms:
1.98 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
1.98 + -1x + -1x2 = 0 + x2 + -1x2
1.98 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1.98 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-1.98 + x + x2 = 0

Move the constant term to the right:

Add '1.98' to each side of the equation.
-1.98 + x + 1.98 + x2 = 0 + 1.98

Reorder the terms:
-1.98 + 1.98 + x + x2 = 0 + 1.98

Combine like terms: -1.98 + 1.98 = 0.00
0.00 + x + x2 = 0 + 1.98
x + x2 = 0 + 1.98

Combine like terms: 0 + 1.98 = 1.98
x + x2 = 1.98

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 = 1.98 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.98 + 0.25

Combine like terms: 1.98 + 0.25 = 2.23
1.25 + x2 = 2.23

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.23

Calculate the square root of the right side: 1.493318452

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.493318452 and -1.493318452.

Subproblem 1
x + 0.5 = 1.493318452

Simplifying
x + 0.5 = 1.493318452

Reorder the terms:
0.5 + x = 1.493318452

Solving
0.5 + x = 1.493318452

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 = 1.493318452 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.493318452 + -0.5
x = 1.493318452 + -0.5

Combine like terms: 1.493318452 + -0.5 = 0.993318452
x = 0.993318452

Simplifying
x = 0.993318452

Subproblem 2
x + 0.5 = -1.493318452

Simplifying
x + 0.5 = -1.493318452

Reorder the terms:
0.5 + x = -1.493318452

Solving
0.5 + x = -1.493318452

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 = -1.493318452 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.493318452 + -0.5
x = -1.493318452 + -0.5

Combine like terms: -1.493318452 + -0.5 = -1.993318452
x = -1.993318452

Simplifying
x = -1.993318452

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.993318452, -1.993318452}