-10x^2+225x-1025=0

Solution for -10x^2+225x-1025=0 equation:

Simplifying
-10x2 + 225x + -1025 = 0

Reorder the terms:
-1025 + 225x + -10x2 = 0

Solving
-1025 + 225x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-205 + 45x + -2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-205 + 45x + -2x2)' equal to zero and attempt to solve:

Simplifying
-205 + 45x + -2x2 = 0

Solving
-205 + 45x + -2x2 = 0

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

Divide each side by '-2'.
102.5 + -22.5x + x2 = 0

Move the constant term to the right:

Add '-102.5' to each side of the equation.
102.5 + -22.5x + -102.5 + x2 = 0 + -102.5

Reorder the terms:
102.5 + -102.5 + -22.5x + x2 = 0 + -102.5

Combine like terms: 102.5 + -102.5 = 0.0
0.0 + -22.5x + x2 = 0 + -102.5
-22.5x + x2 = 0 + -102.5

Combine like terms: 0 + -102.5 = -102.5
-22.5x + x2 = -102.5

The x term is -22.5x.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5x + 126.5625 + x2 = -102.5 + 126.5625

Reorder the terms:
126.5625 + -22.5x + x2 = -102.5 + 126.5625

Combine like terms: -102.5 + 126.5625 = 24.0625
126.5625 + -22.5x + x2 = 24.0625

Factor a perfect square on the left side:
(x + -11.25)(x + -11.25) = 24.0625

Calculate the square root of the right side: 4.905354218

Break this problem into two subproblems by setting 
(x + -11.25) equal to 4.905354218 and -4.905354218.

Subproblem 1
x + -11.25 = 4.905354218

Simplifying
x + -11.25 = 4.905354218

Reorder the terms:
-11.25 + x = 4.905354218

Solving
-11.25 + x = 4.905354218

Solving for variable 'x'.

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

Add '11.25' to each side of the equation.
-11.25 + 11.25 + x = 4.905354218 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + x = 4.905354218 + 11.25
x = 4.905354218 + 11.25

Combine like terms: 4.905354218 + 11.25 = 16.155354218
x = 16.155354218

Simplifying
x = 16.155354218

Subproblem 2
x + -11.25 = -4.905354218

Simplifying
x + -11.25 = -4.905354218

Reorder the terms:
-11.25 + x = -4.905354218

Solving
-11.25 + x = -4.905354218

Solving for variable 'x'.

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

Add '11.25' to each side of the equation.
-11.25 + 11.25 + x = -4.905354218 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + x = -4.905354218 + 11.25
x = -4.905354218 + 11.25

Combine like terms: -4.905354218 + 11.25 = 6.344645782
x = 6.344645782

Simplifying
x = 6.344645782

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.155354218, 6.344645782}
Solution
x = {16.155354218, 6.344645782}