2-6x(x-6)=22

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Solution for 2-6x(x-6)=22 equation: 


Simplifying
2 + -6x(x + -6) = 22

Reorder the terms:
2 + -6x(-6 + x) = 22
2 + (-6 * -6x + x * -6x) = 22
2 + (36x + -6x2) = 22

Solving
2 + 36x + -6x2 = 22

Solving for variable 'x'.

Reorder the terms:
2 + -22 + 36x + -6x2 = 22 + -22

Combine like terms: 2 + -22 = -20
-20 + 36x + -6x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-20 + 36x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 18x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 18x + -3x2)' equal to zero and attempt to solve:

Simplifying
-10 + 18x + -3x2 = 0

Solving
-10 + 18x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
3.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -6x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -6x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + -3.333333333
-6x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-6x + x2 = -3.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -3.333333333 + 9

Reorder the terms:
9 + -6x + x2 = -3.333333333 + 9

Combine like terms: -3.333333333 + 9 = 5.666666667
9 + -6x + x2 = 5.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5.666666667

Calculate the square root of the right side: 2.380476143

Break this problem into two subproblems by setting 
(x + -3) equal to 2.380476143 and -2.380476143.


Subproblem 1
x + -3 = 2.380476143

Simplifying
x + -3 = 2.380476143

Reorder the terms:
-3 + x = 2.380476143

Solving
-3 + x = 2.380476143

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.380476143 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.380476143 + 3
x = 2.380476143 + 3

Combine like terms: 2.380476143 + 3 = 5.380476143
x = 5.380476143

Simplifying
x = 5.380476143


Subproblem 2
x + -3 = -2.380476143

Simplifying
x + -3 = -2.380476143

Reorder the terms:
-3 + x = -2.380476143

Solving
-3 + x = -2.380476143

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.380476143 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.380476143 + 3
x = -2.380476143 + 3

Combine like terms: -2.380476143 + 3 = 0.619523857
x = 0.619523857

Simplifying
x = 0.619523857


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.380476143, 0.619523857}
Solution
x = {5.380476143, 0.619523857}

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