(3.4)=(X+1)X

Solution for (3.4)=(X+1)X equation:

Simplifying
(3.4) = (X + 1) * X
3.4 = (X + 1) * X

Reorder the terms:
3.4 = (1 + X) * X

Reorder the terms for easier multiplication:
3.4 = X(1 + X)
3.4 = (1 * X + X * X)
3.4 = (1X + X2)

Solving
3.4 = 1X + X2

Solving for variable 'X'.

Reorder the terms:
3.4 + -1X + -1X2 = 1X + -1X + X2 + -1X2

Combine like terms: 1X + -1X = 0
3.4 + -1X + -1X2 = 0 + X2 + -1X2
3.4 + -1X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
3.4 + -1X + -1X2 = 0

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

Divide each side by '-1'.
-3.4 + X + X2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + X + 3.4 + X2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + X + X2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + X + X2 = 0 + 3.4
X + X2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
X + X2 = 3.4

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 = 3.4 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + X2 = 3.4 + 0.25

Combine like terms: 3.4 + 0.25 = 3.65
1.25 + X2 = 3.65

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 3.65

Calculate the square root of the right side: 1.910497317

Break this problem into two subproblems by setting 
(X + 0.5) equal to 1.910497317 and -1.910497317.

Subproblem 1
X + 0.5 = 1.910497317

Simplifying
X + 0.5 = 1.910497317

Reorder the terms:
0.5 + X = 1.910497317

Solving
0.5 + X = 1.910497317

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 = 1.910497317 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 1.910497317 + -0.5
X = 1.910497317 + -0.5

Combine like terms: 1.910497317 + -0.5 = 1.410497317
X = 1.410497317

Simplifying
X = 1.410497317

Subproblem 2
X + 0.5 = -1.910497317

Simplifying
X + 0.5 = -1.910497317

Reorder the terms:
0.5 + X = -1.910497317

Solving
0.5 + X = -1.910497317

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 = -1.910497317 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -1.910497317 + -0.5
X = -1.910497317 + -0.5

Combine like terms: -1.910497317 + -0.5 = -2.410497317
X = -2.410497317

Simplifying
X = -2.410497317

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.410497317, -2.410497317}