x=0.25*((0.85*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5))

Solution for x=0.25*((0.85*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5)) equation:

Simplifying
x = 0.25((0.85(15 + -1.75x) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((15 * 0.85 + -1.75x * 0.85) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((12.75 + -1.4875x) + -2.5)(0.85(15 + -1.75x) + -2.5))

Reorder the terms:
x = 0.25((12.75 + -2.5 + -1.4875x)(0.85(15 + -1.75x) + -2.5))

Combine like terms: 12.75 + -2.5 = 10.25
x = 0.25((10.25 + -1.4875x)(0.85(15 + -1.75x) + -2.5))
x = 0.25((10.25 + -1.4875x)((15 * 0.85 + -1.75x * 0.85) + -2.5))
x = 0.25((10.25 + -1.4875x)((12.75 + -1.4875x) + -2.5))

Reorder the terms:
x = 0.25((10.25 + -1.4875x)(12.75 + -2.5 + -1.4875x))

Combine like terms: 12.75 + -2.5 = 10.25
x = 0.25((10.25 + -1.4875x)(10.25 + -1.4875x))

Multiply (10.25 + -1.4875x) * (10.25 + -1.4875x)
x = 0.25((10.25(10.25 + -1.4875x) + -1.4875x * (10.25 + -1.4875x)))
x = 0.25(((10.25 * 10.25 + -1.4875x * 10.25) + -1.4875x * (10.25 + -1.4875x)))
x = 0.25(((105.0625 + -15.246875x) + -1.4875x * (10.25 + -1.4875x)))
x = 0.25((105.0625 + -15.246875x + (10.25 * -1.4875x + -1.4875x * -1.4875x)))
x = 0.25((105.0625 + -15.246875x + (-15.246875x + 2.21265625x2)))

Combine like terms: -15.246875x + -15.246875x = -30.49375x
x = 0.25((105.0625 + -30.49375x + 2.21265625x2))
x = (105.0625 * 0.25 + -30.49375x * 0.25 + 2.21265625x2 * 0.25)
x = (26.265625 + -7.6234375x + 0.5531640625x2)

Solving
x = 26.265625 + -7.6234375x + 0.5531640625x2

Solving for variable 'x'.

Reorder the terms:
-26.265625 + x + 7.6234375x + -0.5531640625x2 = 26.265625 + -7.6234375x + 0.5531640625x2 + -26.265625 + 7.6234375x + -0.5531640625x2

Combine like terms: x + 7.6234375x = 8.6234375x
-26.265625 + 8.6234375x + -0.5531640625x2 = 26.265625 + -7.6234375x + 0.5531640625x2 + -26.265625 + 7.6234375x + -0.5531640625x2

Reorder the terms:
-26.265625 + 8.6234375x + -0.5531640625x2 = 26.265625 + -26.265625 + -7.6234375x + 7.6234375x + 0.5531640625x2 + -0.5531640625x2

Combine like terms: 26.265625 + -26.265625 = 0.000000
-26.265625 + 8.6234375x + -0.5531640625x2 = 0.000000 + -7.6234375x + 7.6234375x + 0.5531640625x2 + -0.5531640625x2
-26.265625 + 8.6234375x + -0.5531640625x2 = -7.6234375x + 7.6234375x + 0.5531640625x2 + -0.5531640625x2

Combine like terms: -7.6234375x + 7.6234375x = 0.0000000
-26.265625 + 8.6234375x + -0.5531640625x2 = 0.0000000 + 0.5531640625x2 + -0.5531640625x2
-26.265625 + 8.6234375x + -0.5531640625x2 = 0.5531640625x2 + -0.5531640625x2

Combine like terms: 0.5531640625x2 + -0.5531640625x2 = 0.0000000000
-26.265625 + 8.6234375x + -0.5531640625x2 = 0.0000000000

Begin completing the square.  Divide all terms by
-0.5531640625 the coefficient of the squared term: 

Divide each side by '-0.5531640625'.
47.48252242 + -15.58929454x + x2 = 0

Move the constant term to the right:

Add '-47.48252242' to each side of the equation.
47.48252242 + -15.58929454x + -47.48252242 + x2 = 0 + -47.48252242

Reorder the terms:
47.48252242 + -47.48252242 + -15.58929454x + x2 = 0 + -47.48252242

Combine like terms: 47.48252242 + -47.48252242 = 0.00000000
0.00000000 + -15.58929454x + x2 = 0 + -47.48252242
-15.58929454x + x2 = 0 + -47.48252242

Combine like terms: 0 + -47.48252242 = -47.48252242
-15.58929454x + x2 = -47.48252242

The x term is -15.58929454x.  Take half its coefficient (-7.79464727).
Square it (60.75652606) and add it to both sides.

Add '60.75652606' to each side of the equation.
-15.58929454x + 60.75652606 + x2 = -47.48252242 + 60.75652606

Reorder the terms:
60.75652606 + -15.58929454x + x2 = -47.48252242 + 60.75652606

Combine like terms: -47.48252242 + 60.75652606 = 13.27400364
60.75652606 + -15.58929454x + x2 = 13.27400364

Factor a perfect square on the left side:
(x + -7.79464727)(x + -7.79464727) = 13.27400364

Calculate the square root of the right side: 3.643350606

Break this problem into two subproblems by setting 
(x + -7.79464727) equal to 3.643350606 and -3.643350606.

Subproblem 1
x + -7.79464727 = 3.643350606

Simplifying
x + -7.79464727 = 3.643350606

Reorder the terms:
-7.79464727 + x = 3.643350606

Solving
-7.79464727 + x = 3.643350606

Solving for variable 'x'.

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

Add '7.79464727' to each side of the equation.
-7.79464727 + 7.79464727 + x = 3.643350606 + 7.79464727

Combine like terms: -7.79464727 + 7.79464727 = 0.00000000
0.00000000 + x = 3.643350606 + 7.79464727
x = 3.643350606 + 7.79464727

Combine like terms: 3.643350606 + 7.79464727 = 11.437997876
x = 11.437997876

Simplifying
x = 11.437997876

Subproblem 2
x + -7.79464727 = -3.643350606

Simplifying
x + -7.79464727 = -3.643350606

Reorder the terms:
-7.79464727 + x = -3.643350606

Solving
-7.79464727 + x = -3.643350606

Solving for variable 'x'.

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

Add '7.79464727' to each side of the equation.
-7.79464727 + 7.79464727 + x = -3.643350606 + 7.79464727

Combine like terms: -7.79464727 + 7.79464727 = 0.00000000
0.00000000 + x = -3.643350606 + 7.79464727
x = -3.643350606 + 7.79464727

Combine like terms: -3.643350606 + 7.79464727 = 4.151296664
x = 4.151296664

Simplifying
x = 4.151296664

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.437997876, 4.151296664}