(22-2x)(10-2x)=180

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Solution for (22-2x)(10-2x)=180 equation: 


Simplifying
(22 + -2x)(10 + -2x) = 180

Multiply (22 + -2x) * (10 + -2x)
(22(10 + -2x) + -2x * (10 + -2x)) = 180
((10 * 22 + -2x * 22) + -2x * (10 + -2x)) = 180
((220 + -44x) + -2x * (10 + -2x)) = 180
(220 + -44x + (10 * -2x + -2x * -2x)) = 180
(220 + -44x + (-20x + 4x2)) = 180

Combine like terms: -44x + -20x = -64x
(220 + -64x + 4x2) = 180

Solving
220 + -64x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
220 + -180 + -64x + 4x2 = 180 + -180

Combine like terms: 220 + -180 = 40
40 + -64x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
40 + -64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(10 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -16x + x2 = 0

Solving
10 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -16x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -16x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -16x + x2 = 0 + -10
-16x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-16x + x2 = -10

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -10 + 64

Reorder the terms:
64 + -16x + x2 = -10 + 64

Combine like terms: -10 + 64 = 54
64 + -16x + x2 = 54

Factor a perfect square on the left side:
(x + -8)(x + -8) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + -8) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + -8 = 7.348469228

Simplifying
x + -8 = 7.348469228

Reorder the terms:
-8 + x = 7.348469228

Solving
-8 + x = 7.348469228

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.348469228 + 8
x = 7.348469228 + 8

Combine like terms: 7.348469228 + 8 = 15.348469228
x = 15.348469228

Simplifying
x = 15.348469228


Subproblem 2
x + -8 = -7.348469228

Simplifying
x + -8 = -7.348469228

Reorder the terms:
-8 + x = -7.348469228

Solving
-8 + x = -7.348469228

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.348469228 + 8
x = -7.348469228 + 8

Combine like terms: -7.348469228 + 8 = 0.651530772
x = 0.651530772

Simplifying
x = 0.651530772


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.348469228, 0.651530772}
Solution
x = {15.348469228, 0.651530772}

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