-50x^2+3500x-52500=0

Solution for -50x^2+3500x-52500=0 equation:

Simplifying
-50x2 + 3500x + -52500 = 0

Reorder the terms:
-52500 + 3500x + -50x2 = 0

Solving
-52500 + 3500x + -50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '50'.
50(-1050 + 70x + -1x2) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-1050 + 70x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1050 + 70x + -1x2 = 0

Solving
-1050 + 70x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1050 + -70x + x2 = 0

Move the constant term to the right:

Add '-1050' to each side of the equation.
1050 + -70x + -1050 + x2 = 0 + -1050

Reorder the terms:
1050 + -1050 + -70x + x2 = 0 + -1050

Combine like terms: 1050 + -1050 = 0
0 + -70x + x2 = 0 + -1050
-70x + x2 = 0 + -1050

Combine like terms: 0 + -1050 = -1050
-70x + x2 = -1050

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = -1050 + 1225

Reorder the terms:
1225 + -70x + x2 = -1050 + 1225

Combine like terms: -1050 + 1225 = 175
1225 + -70x + x2 = 175

Factor a perfect square on the left side:
(x + -35)(x + -35) = 175

Calculate the square root of the right side: 13.228756555

Break this problem into two subproblems by setting 
(x + -35) equal to 13.228756555 and -13.228756555.

Subproblem 1
x + -35 = 13.228756555

Simplifying
x + -35 = 13.228756555

Reorder the terms:
-35 + x = 13.228756555

Solving
-35 + x = 13.228756555

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = 13.228756555 + 35

Combine like terms: -35 + 35 = 0
0 + x = 13.228756555 + 35
x = 13.228756555 + 35

Combine like terms: 13.228756555 + 35 = 48.228756555
x = 48.228756555

Simplifying
x = 48.228756555

Subproblem 2
x + -35 = -13.228756555

Simplifying
x + -35 = -13.228756555

Reorder the terms:
-35 + x = -13.228756555

Solving
-35 + x = -13.228756555

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = -13.228756555 + 35

Combine like terms: -35 + 35 = 0
0 + x = -13.228756555 + 35
x = -13.228756555 + 35

Combine like terms: -13.228756555 + 35 = 21.771243445
x = 21.771243445

Simplifying
x = 21.771243445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.228756555, 21.771243445}
Solution
x = {48.228756555, 21.771243445}