x+[x+x]*x=74

Solution for x+[x+x]*x=74 equation:

Simplifying
x + [x + x] * x = 74

Combine like terms: x + x = 2x
x + [2x] * x = 74

Remove brackets around [2x]
x + 2x * x = 74

Multiply x * x
x + 2x2 = 74

Solving
x + 2x2 = 74

Solving for variable 'x'.

Reorder the terms:
-74 + x + 2x2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + x + 2x2 = 0

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

Divide each side by '2'.
-37 + 0.5x + x2 = 0

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 0.5x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 0.5x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 0.5x + x2 = 0 + 37
0.5x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
0.5x + x2 = 37

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.
0.5x + 0.25 + x2 = 37 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 37 + 0.25

Combine like terms: 37 + 0.25 = 37.25
0.25 + 0.5x + x2 = 37.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.103277808 and -6.103277808.

Subproblem 1
x + 0.5 = 6.103277808

Simplifying
x + 0.5 = 6.103277808

Reorder the terms:
0.5 + x = 6.103277808

Solving
0.5 + x = 6.103277808

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 = 6.103277808 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.103277808 + -0.5
x = 6.103277808 + -0.5

Combine like terms: 6.103277808 + -0.5 = 5.603277808
x = 5.603277808

Simplifying
x = 5.603277808

Subproblem 2
x + 0.5 = -6.103277808

Simplifying
x + 0.5 = -6.103277808

Reorder the terms:
0.5 + x = -6.103277808

Solving
0.5 + x = -6.103277808

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 = -6.103277808 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.103277808 + -0.5
x = -6.103277808 + -0.5

Combine like terms: -6.103277808 + -0.5 = -6.603277808
x = -6.603277808

Simplifying
x = -6.603277808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.603277808, -6.603277808}