x=0.25*((0.085*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5))

Solution for x=0.25*((0.085*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5)) equation:

Simplifying
x = 0.25((0.085(15 + -1.75x) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((15 * 0.085 + -1.75x * 0.085) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((1.275 + -0.14875x) + -2.5)(0.85(15 + -1.75x) + -2.5))

Reorder the terms:
x = 0.25((1.275 + -2.5 + -0.14875x)(0.85(15 + -1.75x) + -2.5))

Combine like terms: 1.275 + -2.5 = -1.225
x = 0.25((-1.225 + -0.14875x)(0.85(15 + -1.75x) + -2.5))
x = 0.25((-1.225 + -0.14875x)((15 * 0.85 + -1.75x * 0.85) + -2.5))
x = 0.25((-1.225 + -0.14875x)((12.75 + -1.4875x) + -2.5))

Reorder the terms:
x = 0.25((-1.225 + -0.14875x)(12.75 + -2.5 + -1.4875x))

Combine like terms: 12.75 + -2.5 = 10.25
x = 0.25((-1.225 + -0.14875x)(10.25 + -1.4875x))

Multiply (-1.225 + -0.14875x) * (10.25 + -1.4875x)
x = 0.25((-1.225(10.25 + -1.4875x) + -0.14875x * (10.25 + -1.4875x)))
x = 0.25(((10.25 * -1.225 + -1.4875x * -1.225) + -0.14875x * (10.25 + -1.4875x)))
x = 0.25(((-12.55625 + 1.8221875x) + -0.14875x * (10.25 + -1.4875x)))
x = 0.25((-12.55625 + 1.8221875x + (10.25 * -0.14875x + -1.4875x * -0.14875x)))
x = 0.25((-12.55625 + 1.8221875x + (-1.5246875x + 0.221265625x2)))

Combine like terms: 1.8221875x + -1.5246875x = 0.2975x
x = 0.25((-12.55625 + 0.2975x + 0.221265625x2))
x = (-12.55625 * 0.25 + 0.2975x * 0.25 + 0.221265625x2 * 0.25)
x = (-3.1390625 + 0.074375x + 0.05531640625x2)

Solving
x = -3.1390625 + 0.074375x + 0.05531640625x2

Solving for variable 'x'.

Reorder the terms:
3.1390625 + x + -0.074375x + -0.05531640625x2 = -3.1390625 + 0.074375x + 0.05531640625x2 + 3.1390625 + -0.074375x + -0.05531640625x2

Combine like terms: x + -0.074375x = 0.925625x
3.1390625 + 0.925625x + -0.05531640625x2 = -3.1390625 + 0.074375x + 0.05531640625x2 + 3.1390625 + -0.074375x + -0.05531640625x2

Reorder the terms:
3.1390625 + 0.925625x + -0.05531640625x2 = -3.1390625 + 3.1390625 + 0.074375x + -0.074375x + 0.05531640625x2 + -0.05531640625x2

Combine like terms: -3.1390625 + 3.1390625 = 0.0000000
3.1390625 + 0.925625x + -0.05531640625x2 = 0.0000000 + 0.074375x + -0.074375x + 0.05531640625x2 + -0.05531640625x2
3.1390625 + 0.925625x + -0.05531640625x2 = 0.074375x + -0.074375x + 0.05531640625x2 + -0.05531640625x2

Combine like terms: 0.074375x + -0.074375x = 0.000000
3.1390625 + 0.925625x + -0.05531640625x2 = 0.000000 + 0.05531640625x2 + -0.05531640625x2
3.1390625 + 0.925625x + -0.05531640625x2 = 0.05531640625x2 + -0.05531640625x2

Combine like terms: 0.05531640625x2 + -0.05531640625x2 = 0.00000000000
3.1390625 + 0.925625x + -0.05531640625x2 = 0.00000000000

Begin completing the square.  Divide all terms by
-0.05531640625 the coefficient of the squared term: 

Divide each side by '-0.05531640625'.
-56.74740484 + -16.73328155x + x2 = 0

Move the constant term to the right:

Add '56.74740484' to each side of the equation.
-56.74740484 + -16.73328155x + 56.74740484 + x2 = 0 + 56.74740484

Reorder the terms:
-56.74740484 + 56.74740484 + -16.73328155x + x2 = 0 + 56.74740484

Combine like terms: -56.74740484 + 56.74740484 = 0.00000000
0.00000000 + -16.73328155x + x2 = 0 + 56.74740484
-16.73328155x + x2 = 0 + 56.74740484

Combine like terms: 0 + 56.74740484 = 56.74740484
-16.73328155x + x2 = 56.74740484

The x term is -16.73328155x.  Take half its coefficient (-8.366640775).
Square it (70.00067786) and add it to both sides.

Add '70.00067786' to each side of the equation.
-16.73328155x + 70.00067786 + x2 = 56.74740484 + 70.00067786

Reorder the terms:
70.00067786 + -16.73328155x + x2 = 56.74740484 + 70.00067786

Combine like terms: 56.74740484 + 70.00067786 = 126.7480827
70.00067786 + -16.73328155x + x2 = 126.7480827

Factor a perfect square on the left side:
(x + -8.366640775)(x + -8.366640775) = 126.7480827

Calculate the square root of the right side: 11.258245099

Break this problem into two subproblems by setting 
(x + -8.366640775) equal to 11.258245099 and -11.258245099.

Subproblem 1
x + -8.366640775 = 11.258245099

Simplifying
x + -8.366640775 = 11.258245099

Reorder the terms:
-8.366640775 + x = 11.258245099

Solving
-8.366640775 + x = 11.258245099

Solving for variable 'x'.

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

Add '8.366640775' to each side of the equation.
-8.366640775 + 8.366640775 + x = 11.258245099 + 8.366640775

Combine like terms: -8.366640775 + 8.366640775 = 0.000000000
0.000000000 + x = 11.258245099 + 8.366640775
x = 11.258245099 + 8.366640775

Combine like terms: 11.258245099 + 8.366640775 = 19.624885874
x = 19.624885874

Simplifying
x = 19.624885874

Subproblem 2
x + -8.366640775 = -11.258245099

Simplifying
x + -8.366640775 = -11.258245099

Reorder the terms:
-8.366640775 + x = -11.258245099

Solving
-8.366640775 + x = -11.258245099

Solving for variable 'x'.

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

Add '8.366640775' to each side of the equation.
-8.366640775 + 8.366640775 + x = -11.258245099 + 8.366640775

Combine like terms: -8.366640775 + 8.366640775 = 0.000000000
0.000000000 + x = -11.258245099 + 8.366640775
x = -11.258245099 + 8.366640775

Combine like terms: -11.258245099 + 8.366640775 = -2.891604324
x = -2.891604324

Simplifying
x = -2.891604324

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.624885874, -2.891604324}