0=7(.25-x)(055-x)-2x^2

Solution for 0=7(.25-x)(055-x)-2x^2 equation:

Simplifying
0 = 7(0.25 + -1x)(55 + -1x) + -2x2

Multiply (0.25 + -1x) * (55 + -1x)
0 = 7(0.25(55 + -1x) + -1x * (55 + -1x)) + -2x2
0 = 7((55 * 0.25 + -1x * 0.25) + -1x * (55 + -1x)) + -2x2
0 = 7((13.75 + -0.25x) + -1x * (55 + -1x)) + -2x2
0 = 7(13.75 + -0.25x + (55 * -1x + -1x * -1x)) + -2x2
0 = 7(13.75 + -0.25x + (-55x + 1x2)) + -2x2

Combine like terms: -0.25x + -55x = -55.25x
0 = 7(13.75 + -55.25x + 1x2) + -2x2
0 = (13.75 * 7 + -55.25x * 7 + 1x2 * 7) + -2x2
0 = (96.25 + -386.75x + 7x2) + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
0 = 96.25 + -386.75x + 5x2

Solving
0 = 96.25 + -386.75x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -96.25 = -96.25
-96.25 + 386.75x + -5x2 = 96.25 + -386.75x + 5x2 + -96.25 + 386.75x + -5x2

Reorder the terms:
-96.25 + 386.75x + -5x2 = 96.25 + -96.25 + -386.75x + 386.75x + 5x2 + -5x2

Combine like terms: 96.25 + -96.25 = 0.00
-96.25 + 386.75x + -5x2 = 0.00 + -386.75x + 386.75x + 5x2 + -5x2
-96.25 + 386.75x + -5x2 = -386.75x + 386.75x + 5x2 + -5x2

Combine like terms: -386.75x + 386.75x = 0.00
-96.25 + 386.75x + -5x2 = 0.00 + 5x2 + -5x2
-96.25 + 386.75x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-96.25 + 386.75x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
19.25 + -77.35x + x2 = 0

Move the constant term to the right:

Add '-19.25' to each side of the equation.
19.25 + -77.35x + -19.25 + x2 = 0 + -19.25

Reorder the terms:
19.25 + -19.25 + -77.35x + x2 = 0 + -19.25

Combine like terms: 19.25 + -19.25 = 0.00
0.00 + -77.35x + x2 = 0 + -19.25
-77.35x + x2 = 0 + -19.25

Combine like terms: 0 + -19.25 = -19.25
-77.35x + x2 = -19.25

The x term is -77.35x.  Take half its coefficient (-38.675).
Square it (1495.755625) and add it to both sides.

Add '1495.755625' to each side of the equation.
-77.35x + 1495.755625 + x2 = -19.25 + 1495.755625

Reorder the terms:
1495.755625 + -77.35x + x2 = -19.25 + 1495.755625

Combine like terms: -19.25 + 1495.755625 = 1476.505625
1495.755625 + -77.35x + x2 = 1476.505625

Factor a perfect square on the left side:
(x + -38.675)(x + -38.675) = 1476.505625

Calculate the square root of the right side: 38.425325308

Break this problem into two subproblems by setting 
(x + -38.675) equal to 38.425325308 and -38.425325308.

Subproblem 1
x + -38.675 = 38.425325308

Simplifying
x + -38.675 = 38.425325308

Reorder the terms:
-38.675 + x = 38.425325308

Solving
-38.675 + x = 38.425325308

Solving for variable 'x'.

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

Add '38.675' to each side of the equation.
-38.675 + 38.675 + x = 38.425325308 + 38.675

Combine like terms: -38.675 + 38.675 = 0.000
0.000 + x = 38.425325308 + 38.675
x = 38.425325308 + 38.675

Combine like terms: 38.425325308 + 38.675 = 77.100325308
x = 77.100325308

Simplifying
x = 77.100325308

Subproblem 2
x + -38.675 = -38.425325308

Simplifying
x + -38.675 = -38.425325308

Reorder the terms:
-38.675 + x = -38.425325308

Solving
-38.675 + x = -38.425325308

Solving for variable 'x'.

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

Add '38.675' to each side of the equation.
-38.675 + 38.675 + x = -38.425325308 + 38.675

Combine like terms: -38.675 + 38.675 = 0.000
0.000 + x = -38.425325308 + 38.675
x = -38.425325308 + 38.675

Combine like terms: -38.425325308 + 38.675 = 0.249674692
x = 0.249674692

Simplifying
x = 0.249674692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {77.100325308, 0.249674692}