1.67=x^2+x

Solution for 1.67=x^2+x equation:

Simplifying
1.67 = x2 + x

Reorder the terms:
1.67 = x + x2

Solving
1.67 = x + x2

Solving for variable 'x'.

Reorder the terms:
1.67 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
1.67 + -1x + -1x2 = 0 + x2 + -1x2
1.67 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1.67 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-1.67 + x + x2 = 0

Move the constant term to the right:

Add '1.67' to each side of the equation.
-1.67 + x + 1.67 + x2 = 0 + 1.67

Reorder the terms:
-1.67 + 1.67 + x + x2 = 0 + 1.67

Combine like terms: -1.67 + 1.67 = 0.00
0.00 + x + x2 = 0 + 1.67
x + x2 = 0 + 1.67

Combine like terms: 0 + 1.67 = 1.67
x + x2 = 1.67

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 = 1.67 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.67 + 0.25

Combine like terms: 1.67 + 0.25 = 1.92
1.25 + x2 = 1.92

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.92

Calculate the square root of the right side: 1.385640646

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.385640646 and -1.385640646.

Subproblem 1
x + 0.5 = 1.385640646

Simplifying
x + 0.5 = 1.385640646

Reorder the terms:
0.5 + x = 1.385640646

Solving
0.5 + x = 1.385640646

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 = 1.385640646 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.385640646 + -0.5
x = 1.385640646 + -0.5

Combine like terms: 1.385640646 + -0.5 = 0.885640646
x = 0.885640646

Simplifying
x = 0.885640646

Subproblem 2
x + 0.5 = -1.385640646

Simplifying
x + 0.5 = -1.385640646

Reorder the terms:
0.5 + x = -1.385640646

Solving
0.5 + x = -1.385640646

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 = -1.385640646 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.385640646 + -0.5
x = -1.385640646 + -0.5

Combine like terms: -1.385640646 + -0.5 = -1.885640646
x = -1.885640646

Simplifying
x = -1.885640646

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.885640646, -1.885640646}