0.08x(x-100)=65.5-0.07x

Solution for 0.08x(x-100)=65.5-0.07x equation:

Simplifying
0.08x(x + -100) = 65.5 + -0.07x

Reorder the terms:
0.08x(-100 + x) = 65.5 + -0.07x
(-100 * 0.08x + x * 0.08x) = 65.5 + -0.07x
(-8x + 0.08x2) = 65.5 + -0.07x

Solving
-8x + 0.08x2 = 65.5 + -0.07x

Solving for variable 'x'.

Reorder the terms:
-65.5 + -8x + 0.07x + 0.08x2 = 65.5 + -0.07x + -65.5 + 0.07x

Combine like terms: -8x + 0.07x = -7.93x
-65.5 + -7.93x + 0.08x2 = 65.5 + -0.07x + -65.5 + 0.07x

Reorder the terms:
-65.5 + -7.93x + 0.08x2 = 65.5 + -65.5 + -0.07x + 0.07x

Combine like terms: 65.5 + -65.5 = 0.0
-65.5 + -7.93x + 0.08x2 = 0.0 + -0.07x + 0.07x
-65.5 + -7.93x + 0.08x2 = -0.07x + 0.07x

Combine like terms: -0.07x + 0.07x = 0.00
-65.5 + -7.93x + 0.08x2 = 0.00

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

Divide each side by '0.08'.
-818.75 + -99.125x + x2 = 0

Move the constant term to the right:

Add '818.75' to each side of the equation.
-818.75 + -99.125x + 818.75 + x2 = 0 + 818.75

Reorder the terms:
-818.75 + 818.75 + -99.125x + x2 = 0 + 818.75

Combine like terms: -818.75 + 818.75 = 0.00
0.00 + -99.125x + x2 = 0 + 818.75
-99.125x + x2 = 0 + 818.75

Combine like terms: 0 + 818.75 = 818.75
-99.125x + x2 = 818.75

The x term is -99.125x.  Take half its coefficient (-49.5625).
Square it (2456.441406) and add it to both sides.

Add '2456.441406' to each side of the equation.
-99.125x + 2456.441406 + x2 = 818.75 + 2456.441406

Reorder the terms:
2456.441406 + -99.125x + x2 = 818.75 + 2456.441406

Combine like terms: 818.75 + 2456.441406 = 3275.191406
2456.441406 + -99.125x + x2 = 3275.191406

Factor a perfect square on the left side:
(x + -49.5625)(x + -49.5625) = 3275.191406

Calculate the square root of the right side: 57.229288009

Break this problem into two subproblems by setting 
(x + -49.5625) equal to 57.229288009 and -57.229288009.

Subproblem 1
x + -49.5625 = 57.229288009

Simplifying
x + -49.5625 = 57.229288009

Reorder the terms:
-49.5625 + x = 57.229288009

Solving
-49.5625 + x = 57.229288009

Solving for variable 'x'.

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

Add '49.5625' to each side of the equation.
-49.5625 + 49.5625 + x = 57.229288009 + 49.5625

Combine like terms: -49.5625 + 49.5625 = 0.0000
0.0000 + x = 57.229288009 + 49.5625
x = 57.229288009 + 49.5625

Combine like terms: 57.229288009 + 49.5625 = 106.791788009
x = 106.791788009

Simplifying
x = 106.791788009

Subproblem 2
x + -49.5625 = -57.229288009

Simplifying
x + -49.5625 = -57.229288009

Reorder the terms:
-49.5625 + x = -57.229288009

Solving
-49.5625 + x = -57.229288009

Solving for variable 'x'.

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

Add '49.5625' to each side of the equation.
-49.5625 + 49.5625 + x = -57.229288009 + 49.5625

Combine like terms: -49.5625 + 49.5625 = 0.0000
0.0000 + x = -57.229288009 + 49.5625
x = -57.229288009 + 49.5625

Combine like terms: -57.229288009 + 49.5625 = -7.666788009
x = -7.666788009

Simplifying
x = -7.666788009

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {106.791788009, -7.666788009}