(80-2x)(90-2x)=7150

Solution for (80-2x)(90-2x)=7150 equation:

Simplifying
(80 + -2x)(90 + -2x) = 7150

Multiply (80 + -2x) * (90 + -2x)
(80(90 + -2x) + -2x * (90 + -2x)) = 7150
((90 * 80 + -2x * 80) + -2x * (90 + -2x)) = 7150
((7200 + -160x) + -2x * (90 + -2x)) = 7150
(7200 + -160x + (90 * -2x + -2x * -2x)) = 7150
(7200 + -160x + (-180x + 4x2)) = 7150

Combine like terms: -160x + -180x = -340x
(7200 + -340x + 4x2) = 7150

Solving
7200 + -340x + 4x2 = 7150

Solving for variable 'x'.

Reorder the terms:
7200 + -7150 + -340x + 4x2 = 7150 + -7150

Combine like terms: 7200 + -7150 = 50
50 + -340x + 4x2 = 7150 + -7150

Combine like terms: 7150 + -7150 = 0
50 + -340x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -170x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(25 + -170x + 2x2)' equal to zero and attempt to solve:

Simplifying
25 + -170x + 2x2 = 0

Solving
25 + -170x + 2x2 = 0

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

Divide each side by '2'.
12.5 + -85x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -85x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -85x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -85x + x2 = 0 + -12.5
-85x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-85x + x2 = -12.5

The x term is -85x.  Take half its coefficient (-42.5).
Square it (1806.25) and add it to both sides.

Add '1806.25' to each side of the equation.
-85x + 1806.25 + x2 = -12.5 + 1806.25

Reorder the terms:
1806.25 + -85x + x2 = -12.5 + 1806.25

Combine like terms: -12.5 + 1806.25 = 1793.75
1806.25 + -85x + x2 = 1793.75

Factor a perfect square on the left side:
(x + -42.5)(x + -42.5) = 1793.75

Calculate the square root of the right side: 42.352685865

Break this problem into two subproblems by setting 
(x + -42.5) equal to 42.352685865 and -42.352685865.

Subproblem 1
x + -42.5 = 42.352685865

Simplifying
x + -42.5 = 42.352685865

Reorder the terms:
-42.5 + x = 42.352685865

Solving
-42.5 + x = 42.352685865

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = 42.352685865 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = 42.352685865 + 42.5
x = 42.352685865 + 42.5

Combine like terms: 42.352685865 + 42.5 = 84.852685865
x = 84.852685865

Simplifying
x = 84.852685865

Subproblem 2
x + -42.5 = -42.352685865

Simplifying
x + -42.5 = -42.352685865

Reorder the terms:
-42.5 + x = -42.352685865

Solving
-42.5 + x = -42.352685865

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = -42.352685865 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = -42.352685865 + 42.5
x = -42.352685865 + 42.5

Combine like terms: -42.352685865 + 42.5 = 0.147314135
x = 0.147314135

Simplifying
x = 0.147314135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {84.852685865, 0.147314135}
Solution
x = {84.852685865, 0.147314135}