11-2x(7-2x)=45

Solution for 11-2x(7-2x)=45 equation:

Simplifying
11 + -2x(7 + -2x) = 45
11 + (7 * -2x + -2x * -2x) = 45
11 + (-14x + 4x2) = 45

Solving
11 + -14x + 4x2 = 45

Solving for variable 'x'.

Reorder the terms:
11 + -45 + -14x + 4x2 = 45 + -45

Combine like terms: 11 + -45 = -34
-34 + -14x + 4x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-34 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -7x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-17 + -7x + 2x2 = 0

Solving
-17 + -7x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + -3.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + -3.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + -3.5x + x2 = 0 + 8.5
-3.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
-3.5x + x2 = 8.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 8.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 8.5 + 3.0625

Combine like terms: 8.5 + 3.0625 = 11.5625
3.0625 + -3.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.400367627 and -3.400367627.

Subproblem 1
x + -1.75 = 3.400367627

Simplifying
x + -1.75 = 3.400367627

Reorder the terms:
-1.75 + x = 3.400367627

Solving
-1.75 + x = 3.400367627

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 3.400367627 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 3.400367627 + 1.75
x = 3.400367627 + 1.75

Combine like terms: 3.400367627 + 1.75 = 5.150367627
x = 5.150367627

Simplifying
x = 5.150367627

Subproblem 2
x + -1.75 = -3.400367627

Simplifying
x + -1.75 = -3.400367627

Reorder the terms:
-1.75 + x = -3.400367627

Solving
-1.75 + x = -3.400367627

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -3.400367627 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -3.400367627 + 1.75
x = -3.400367627 + 1.75

Combine like terms: -3.400367627 + 1.75 = -1.650367627
x = -1.650367627

Simplifying
x = -1.650367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.150367627, -1.650367627}
Solution
x = {5.150367627, -1.650367627}