65.45=(8.5-2x)*(11-2x)

Solution for 65.45=(8.5-2x)*(11-2x) equation:

Simplifying
65.45 = (8.5 + -2x)(11 + -2x)

Multiply (8.5 + -2x) * (11 + -2x)
65.45 = (8.5(11 + -2x) + -2x * (11 + -2x))
65.45 = ((11 * 8.5 + -2x * 8.5) + -2x * (11 + -2x))
65.45 = ((93.5 + -17x) + -2x * (11 + -2x))
65.45 = (93.5 + -17x + (11 * -2x + -2x * -2x))
65.45 = (93.5 + -17x + (-22x + 4x2))

Combine like terms: -17x + -22x = -39x
65.45 = (93.5 + -39x + 4x2)

Solving
65.45 = 93.5 + -39x + 4x2

Solving for variable 'x'.

Combine like terms: 65.45 + -93.5 = -28.05
-28.05 + 39x + -4x2 = 93.5 + -39x + 4x2 + -93.5 + 39x + -4x2

Reorder the terms:
-28.05 + 39x + -4x2 = 93.5 + -93.5 + -39x + 39x + 4x2 + -4x2

Combine like terms: 93.5 + -93.5 = 0.0
-28.05 + 39x + -4x2 = 0.0 + -39x + 39x + 4x2 + -4x2
-28.05 + 39x + -4x2 = -39x + 39x + 4x2 + -4x2

Combine like terms: -39x + 39x = 0
-28.05 + 39x + -4x2 = 0 + 4x2 + -4x2
-28.05 + 39x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-28.05 + 39x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
7.0125 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-7.0125' to each side of the equation.
7.0125 + -9.75x + -7.0125 + x2 = 0 + -7.0125

Reorder the terms:
7.0125 + -7.0125 + -9.75x + x2 = 0 + -7.0125

Combine like terms: 7.0125 + -7.0125 = 0.0000
0.0000 + -9.75x + x2 = 0 + -7.0125
-9.75x + x2 = 0 + -7.0125

Combine like terms: 0 + -7.0125 = -7.0125
-9.75x + x2 = -7.0125

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -7.0125 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -7.0125 + 23.765625

Combine like terms: -7.0125 + 23.765625 = 16.753125
23.765625 + -9.75x + x2 = 16.753125

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 16.753125

Calculate the square root of the right side: 4.093058148

Break this problem into two subproblems by setting 
(x + -4.875) equal to 4.093058148 and -4.093058148.

Subproblem 1
x + -4.875 = 4.093058148

Simplifying
x + -4.875 = 4.093058148

Reorder the terms:
-4.875 + x = 4.093058148

Solving
-4.875 + x = 4.093058148

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = 4.093058148 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = 4.093058148 + 4.875
x = 4.093058148 + 4.875

Combine like terms: 4.093058148 + 4.875 = 8.968058148
x = 8.968058148

Simplifying
x = 8.968058148

Subproblem 2
x + -4.875 = -4.093058148

Simplifying
x + -4.875 = -4.093058148

Reorder the terms:
-4.875 + x = -4.093058148

Solving
-4.875 + x = -4.093058148

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = -4.093058148 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = -4.093058148 + 4.875
x = -4.093058148 + 4.875

Combine like terms: -4.093058148 + 4.875 = 0.781941852
x = 0.781941852

Simplifying
x = 0.781941852

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.968058148, 0.781941852}