x^2-42x+6=0

Solution for x^2-42x+6=0 equation:

Simplifying
x2 + -42x + 6 = 0

Reorder the terms:
6 + -42x + x2 = 0

Solving
6 + -42x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -42x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -42x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -42x + x2 = 0 + -6
-42x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-42x + x2 = -6

The x term is -42x.  Take half its coefficient (-21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
-42x + 441 + x2 = -6 + 441

Reorder the terms:
441 + -42x + x2 = -6 + 441

Combine like terms: -6 + 441 = 435
441 + -42x + x2 = 435

Factor a perfect square on the left side:
(x + -21)(x + -21) = 435

Calculate the square root of the right side: 20.856653615

Break this problem into two subproblems by setting 
(x + -21) equal to 20.856653615 and -20.856653615.

Subproblem 1
x + -21 = 20.856653615

Simplifying
x + -21 = 20.856653615

Reorder the terms:
-21 + x = 20.856653615

Solving
-21 + x = 20.856653615

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '21' to each side of the equation.
-21 + 21 + x = 20.856653615 + 21

Combine like terms: -21 + 21 = 0
0 + x = 20.856653615 + 21
x = 20.856653615 + 21

Combine like terms: 20.856653615 + 21 = 41.856653615
x = 41.856653615

Simplifying
x = 41.856653615

Subproblem 2
x + -21 = -20.856653615

Simplifying
x + -21 = -20.856653615

Reorder the terms:
-21 + x = -20.856653615

Solving
-21 + x = -20.856653615

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '21' to each side of the equation.
-21 + 21 + x = -20.856653615 + 21

Combine like terms: -21 + 21 = 0
0 + x = -20.856653615 + 21
x = -20.856653615 + 21

Combine like terms: -20.856653615 + 21 = 0.143346385
x = 0.143346385

Simplifying
x = 0.143346385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.856653615, 0.143346385}