8.5-8.5x=x*x

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Solution for 8.5-8.5x=x*x equation: 


Simplifying
8.5 + -8.5x = x * x

Multiply x * x
8.5 + -8.5x = x2

Solving
8.5 + -8.5x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
8.5 + -8.5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8.5 + 8.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 8.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 8.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 8.5x + x2 = 0 + 8.5
8.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
8.5x + x2 = 8.5

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 8.5 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 8.5 + 18.0625

Combine like terms: 8.5 + 18.0625 = 26.5625
18.0625 + 8.5x + x2 = 26.5625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 26.5625

Calculate the square root of the right side: 5.153882032

Break this problem into two subproblems by setting 
(x + 4.25) equal to 5.153882032 and -5.153882032.


Subproblem 1
x + 4.25 = 5.153882032

Simplifying
x + 4.25 = 5.153882032

Reorder the terms:
4.25 + x = 5.153882032

Solving
4.25 + x = 5.153882032

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 5.153882032 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 5.153882032 + -4.25
x = 5.153882032 + -4.25

Combine like terms: 5.153882032 + -4.25 = 0.903882032
x = 0.903882032

Simplifying
x = 0.903882032


Subproblem 2
x + 4.25 = -5.153882032

Simplifying
x + 4.25 = -5.153882032

Reorder the terms:
4.25 + x = -5.153882032

Solving
4.25 + x = -5.153882032

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -5.153882032 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -5.153882032 + -4.25
x = -5.153882032 + -4.25

Combine like terms: -5.153882032 + -4.25 = -9.403882032
x = -9.403882032

Simplifying
x = -9.403882032


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.903882032, -9.403882032}

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