0=21(.25-x)(055-x)-2x^2

Solution for 0=21(.25-x)(055-x)-2x^2 equation:

Simplifying
0 = 21(0.25 + -1x)(55 + -1x) + -2x2

Multiply (0.25 + -1x) * (55 + -1x)
0 = 21(0.25(55 + -1x) + -1x * (55 + -1x)) + -2x2
0 = 21((55 * 0.25 + -1x * 0.25) + -1x * (55 + -1x)) + -2x2
0 = 21((13.75 + -0.25x) + -1x * (55 + -1x)) + -2x2
0 = 21(13.75 + -0.25x + (55 * -1x + -1x * -1x)) + -2x2
0 = 21(13.75 + -0.25x + (-55x + 1x2)) + -2x2

Combine like terms: -0.25x + -55x = -55.25x
0 = 21(13.75 + -55.25x + 1x2) + -2x2
0 = (13.75 * 21 + -55.25x * 21 + 1x2 * 21) + -2x2
0 = (288.75 + -1160.25x + 21x2) + -2x2

Combine like terms: 21x2 + -2x2 = 19x2
0 = 288.75 + -1160.25x + 19x2

Solving
0 = 288.75 + -1160.25x + 19x2

Solving for variable 'x'.

Combine like terms: 0 + -288.75 = -288.75
-288.75 + 1160.25x + -19x2 = 288.75 + -1160.25x + 19x2 + -288.75 + 1160.25x + -19x2

Reorder the terms:
-288.75 + 1160.25x + -19x2 = 288.75 + -288.75 + -1160.25x + 1160.25x + 19x2 + -19x2

Combine like terms: 288.75 + -288.75 = 0.00
-288.75 + 1160.25x + -19x2 = 0.00 + -1160.25x + 1160.25x + 19x2 + -19x2
-288.75 + 1160.25x + -19x2 = -1160.25x + 1160.25x + 19x2 + -19x2

Combine like terms: -1160.25x + 1160.25x = 0.00
-288.75 + 1160.25x + -19x2 = 0.00 + 19x2 + -19x2
-288.75 + 1160.25x + -19x2 = 19x2 + -19x2

Combine like terms: 19x2 + -19x2 = 0
-288.75 + 1160.25x + -19x2 = 0

Begin completing the square.  Divide all terms by
-19 the coefficient of the squared term: 

Divide each side by '-19'.
15.19736842 + -61.06578947x + x2 = 0

Move the constant term to the right:

Add '-15.19736842' to each side of the equation.
15.19736842 + -61.06578947x + -15.19736842 + x2 = 0 + -15.19736842

Reorder the terms:
15.19736842 + -15.19736842 + -61.06578947x + x2 = 0 + -15.19736842

Combine like terms: 15.19736842 + -15.19736842 = 0.00000000
0.00000000 + -61.06578947x + x2 = 0 + -15.19736842
-61.06578947x + x2 = 0 + -15.19736842

Combine like terms: 0 + -15.19736842 = -15.19736842
-61.06578947x + x2 = -15.19736842

The x term is -61.06578947x.  Take half its coefficient (-30.53289474).
Square it (932.2576612) and add it to both sides.

Add '932.2576612' to each side of the equation.
-61.06578947x + 932.2576612 + x2 = -15.19736842 + 932.2576612

Reorder the terms:
932.2576612 + -61.06578947x + x2 = -15.19736842 + 932.2576612

Combine like terms: -15.19736842 + 932.2576612 = 917.06029278
932.2576612 + -61.06578947x + x2 = 917.06029278

Factor a perfect square on the left side:
(x + -30.53289474)(x + -30.53289474) = 917.06029278

Calculate the square root of the right side: 30.283003365

Break this problem into two subproblems by setting 
(x + -30.53289474) equal to 30.283003365 and -30.283003365.

Subproblem 1
x + -30.53289474 = 30.283003365

Simplifying
x + -30.53289474 = 30.283003365

Reorder the terms:
-30.53289474 + x = 30.283003365

Solving
-30.53289474 + x = 30.283003365

Solving for variable 'x'.

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

Add '30.53289474' to each side of the equation.
-30.53289474 + 30.53289474 + x = 30.283003365 + 30.53289474

Combine like terms: -30.53289474 + 30.53289474 = 0.00000000
0.00000000 + x = 30.283003365 + 30.53289474
x = 30.283003365 + 30.53289474

Combine like terms: 30.283003365 + 30.53289474 = 60.815898105
x = 60.815898105

Simplifying
x = 60.815898105

Subproblem 2
x + -30.53289474 = -30.283003365

Simplifying
x + -30.53289474 = -30.283003365

Reorder the terms:
-30.53289474 + x = -30.283003365

Solving
-30.53289474 + x = -30.283003365

Solving for variable 'x'.

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

Add '30.53289474' to each side of the equation.
-30.53289474 + 30.53289474 + x = -30.283003365 + 30.53289474

Combine like terms: -30.53289474 + 30.53289474 = 0.00000000
0.00000000 + x = -30.283003365 + 30.53289474
x = -30.283003365 + 30.53289474

Combine like terms: -30.283003365 + 30.53289474 = 0.249891375
x = 0.249891375

Simplifying
x = 0.249891375

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.815898105, 0.249891375}