10x^2-240x+1100=0

Solution for 10x^2-240x+1100=0 equation:

Simplifying
10x2 + -240x + 1100 = 0

Reorder the terms:
1100 + -240x + 10x2 = 0

Solving
1100 + -240x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(110 + -24x + x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(110 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
110 + -24x + x2 = 0

Solving
110 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-110' to each side of the equation.
110 + -24x + -110 + x2 = 0 + -110

Reorder the terms:
110 + -110 + -24x + x2 = 0 + -110

Combine like terms: 110 + -110 = 0
0 + -24x + x2 = 0 + -110
-24x + x2 = 0 + -110

Combine like terms: 0 + -110 = -110
-24x + x2 = -110

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -110 + 144

Reorder the terms:
144 + -24x + x2 = -110 + 144

Combine like terms: -110 + 144 = 34
144 + -24x + x2 = 34

Factor a perfect square on the left side:
(x + -12)(x + -12) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -12) equal to 5.830951895 and -5.830951895.

Subproblem 1
x + -12 = 5.830951895

Simplifying
x + -12 = 5.830951895

Reorder the terms:
-12 + x = 5.830951895

Solving
-12 + x = 5.830951895

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 5.830951895 + 12

Combine like terms: -12 + 12 = 0
0 + x = 5.830951895 + 12
x = 5.830951895 + 12

Combine like terms: 5.830951895 + 12 = 17.830951895
x = 17.830951895

Simplifying
x = 17.830951895

Subproblem 2
x + -12 = -5.830951895

Simplifying
x + -12 = -5.830951895

Reorder the terms:
-12 + x = -5.830951895

Solving
-12 + x = -5.830951895

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -5.830951895 + 12

Combine like terms: -12 + 12 = 0
0 + x = -5.830951895 + 12
x = -5.830951895 + 12

Combine like terms: -5.830951895 + 12 = 6.169048105
x = 6.169048105

Simplifying
x = 6.169048105

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.830951895, 6.169048105}
Solution
x = {17.830951895, 6.169048105}