x(49-.2x)-21=975

Solution for x(49-.2x)-21=975 equation:

Simplifying
x(49 + -0.2x) + -21 = 975
(49 * x + -0.2x * x) + -21 = 975
(49x + -0.2x2) + -21 = 975

Reorder the terms:
-21 + 49x + -0.2x2 = 975

Solving
-21 + 49x + -0.2x2 = 975

Solving for variable 'x'.

Reorder the terms:
-21 + -975 + 49x + -0.2x2 = 975 + -975

Combine like terms: -21 + -975 = -996
-996 + 49x + -0.2x2 = 975 + -975

Combine like terms: 975 + -975 = 0
-996 + 49x + -0.2x2 = 0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
4980 + -245x + x2 = 0

Move the constant term to the right:

Add '-4980' to each side of the equation.
4980 + -245x + -4980 + x2 = 0 + -4980

Reorder the terms:
4980 + -4980 + -245x + x2 = 0 + -4980

Combine like terms: 4980 + -4980 = 0
0 + -245x + x2 = 0 + -4980
-245x + x2 = 0 + -4980

Combine like terms: 0 + -4980 = -4980
-245x + x2 = -4980

The x term is -245x.  Take half its coefficient (-122.5).
Square it (15006.25) and add it to both sides.

Add '15006.25' to each side of the equation.
-245x + 15006.25 + x2 = -4980 + 15006.25

Reorder the terms:
15006.25 + -245x + x2 = -4980 + 15006.25

Combine like terms: -4980 + 15006.25 = 10026.25
15006.25 + -245x + x2 = 10026.25

Factor a perfect square on the left side:
(x + -122.5)(x + -122.5) = 10026.25

Calculate the square root of the right side: 100.13116398

Break this problem into two subproblems by setting 
(x + -122.5) equal to 100.13116398 and -100.13116398.

Subproblem 1
x + -122.5 = 100.13116398

Simplifying
x + -122.5 = 100.13116398

Reorder the terms:
-122.5 + x = 100.13116398

Solving
-122.5 + x = 100.13116398

Solving for variable 'x'.

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

Add '122.5' to each side of the equation.
-122.5 + 122.5 + x = 100.13116398 + 122.5

Combine like terms: -122.5 + 122.5 = 0.0
0.0 + x = 100.13116398 + 122.5
x = 100.13116398 + 122.5

Combine like terms: 100.13116398 + 122.5 = 222.63116398
x = 222.63116398

Simplifying
x = 222.63116398

Subproblem 2
x + -122.5 = -100.13116398

Simplifying
x + -122.5 = -100.13116398

Reorder the terms:
-122.5 + x = -100.13116398

Solving
-122.5 + x = -100.13116398

Solving for variable 'x'.

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

Add '122.5' to each side of the equation.
-122.5 + 122.5 + x = -100.13116398 + 122.5

Combine like terms: -122.5 + 122.5 = 0.0
0.0 + x = -100.13116398 + 122.5
x = -100.13116398 + 122.5

Combine like terms: -100.13116398 + 122.5 = 22.36883602
x = 22.36883602

Simplifying
x = 22.36883602

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {222.63116398, 22.36883602}