(x*x)+x=34

Solution for (x*x)+x=34 equation:

Simplifying
(x * x) + x = 34

Multiply x * x
(x2) + x = 34
x2 + x = 34

Reorder the terms:
x + x2 = 34

Solving
x + x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + x + x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + x + x2 = 0 + 34
x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
x + x2 = 34

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 = 34 + 0.25

Reorder the terms:
0.25 + x + x2 = 34 + 0.25

Combine like terms: 34 + 0.25 = 34.25
0.25 + x + x2 = 34.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.852349955 and -5.852349955.

Subproblem 1
x + 0.5 = 5.852349955

Simplifying
x + 0.5 = 5.852349955

Reorder the terms:
0.5 + x = 5.852349955

Solving
0.5 + x = 5.852349955

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 = 5.852349955 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.852349955 + -0.5
x = 5.852349955 + -0.5

Combine like terms: 5.852349955 + -0.5 = 5.352349955
x = 5.352349955

Simplifying
x = 5.352349955

Subproblem 2
x + 0.5 = -5.852349955

Simplifying
x + 0.5 = -5.852349955

Reorder the terms:
0.5 + x = -5.852349955

Solving
0.5 + x = -5.852349955

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 = -5.852349955 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.852349955 + -0.5
x = -5.852349955 + -0.5

Combine like terms: -5.852349955 + -0.5 = -6.352349955
x = -6.352349955

Simplifying
x = -6.352349955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.352349955, -6.352349955}