2x^2-24x+1=

Solution for 2x^2-24x+1= equation:

Simplifying
2x2 + -24x + 1 = 0

Reorder the terms:
1 + -24x + 2x2 = 0

Solving
1 + -24x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
0.5 + -12x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -12x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -12x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -12x + x2 = 0 + -0.5
-12x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-12x + x2 = -0.5

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -0.5 + 36

Reorder the terms:
36 + -12x + x2 = -0.5 + 36

Combine like terms: -0.5 + 36 = 35.5
36 + -12x + x2 = 35.5

Factor a perfect square on the left side:
(x + -6)(x + -6) = 35.5

Calculate the square root of the right side: 5.958187644

Break this problem into two subproblems by setting 
(x + -6) equal to 5.958187644 and -5.958187644.

Subproblem 1
x + -6 = 5.958187644

Simplifying
x + -6 = 5.958187644

Reorder the terms:
-6 + x = 5.958187644

Solving
-6 + x = 5.958187644

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.958187644 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.958187644 + 6
x = 5.958187644 + 6

Combine like terms: 5.958187644 + 6 = 11.958187644
x = 11.958187644

Simplifying
x = 11.958187644

Subproblem 2
x + -6 = -5.958187644

Simplifying
x + -6 = -5.958187644

Reorder the terms:
-6 + x = -5.958187644

Solving
-6 + x = -5.958187644

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.958187644 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.958187644 + 6
x = -5.958187644 + 6

Combine like terms: -5.958187644 + 6 = 0.041812356
x = 0.041812356

Simplifying
x = 0.041812356

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.958187644, 0.041812356}