11(5X-6)=X(3X-2)

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Solution for 11(5X-6)=X(3X-2) equation: 


Simplifying
11(5X + -6) = X(3X + -2)

Reorder the terms:
11(-6 + 5X) = X(3X + -2)
(-6 * 11 + 5X * 11) = X(3X + -2)
(-66 + 55X) = X(3X + -2)

Reorder the terms:
-66 + 55X = X(-2 + 3X)
-66 + 55X = (-2 * X + 3X * X)
-66 + 55X = (-2X + 3X2)

Solving
-66 + 55X = -2X + 3X2

Solving for variable 'X'.

Combine like terms: 55X + 2X = 57X
-66 + 57X + -3X2 = -2X + 3X2 + 2X + -3X2

Reorder the terms:
-66 + 57X + -3X2 = -2X + 2X + 3X2 + -3X2

Combine like terms: -2X + 2X = 0
-66 + 57X + -3X2 = 0 + 3X2 + -3X2
-66 + 57X + -3X2 = 3X2 + -3X2

Combine like terms: 3X2 + -3X2 = 0
-66 + 57X + -3X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 19X + -1X2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-22 + 19X + -1X2)' equal to zero and attempt to solve:

Simplifying
-22 + 19X + -1X2 = 0

Solving
-22 + 19X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
22 + -19X + X2 = 0

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -19X + -22 + X2 = 0 + -22

Reorder the terms:
22 + -22 + -19X + X2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -19X + X2 = 0 + -22
-19X + X2 = 0 + -22

Combine like terms: 0 + -22 = -22
-19X + X2 = -22

The X term is -19X.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19X + 90.25 + X2 = -22 + 90.25

Reorder the terms:
90.25 + -19X + X2 = -22 + 90.25

Combine like terms: -22 + 90.25 = 68.25
90.25 + -19X + X2 = 68.25

Factor a perfect square on the left side:
(X + -9.5)(X + -9.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(X + -9.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
X + -9.5 = 8.261355821

Simplifying
X + -9.5 = 8.261355821

Reorder the terms:
-9.5 + X = 8.261355821

Solving
-9.5 + X = 8.261355821

Solving for variable 'X'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + X = 8.261355821 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + X = 8.261355821 + 9.5
X = 8.261355821 + 9.5

Combine like terms: 8.261355821 + 9.5 = 17.761355821
X = 17.761355821

Simplifying
X = 17.761355821


Subproblem 2
X + -9.5 = -8.261355821

Simplifying
X + -9.5 = -8.261355821

Reorder the terms:
-9.5 + X = -8.261355821

Solving
-9.5 + X = -8.261355821

Solving for variable 'X'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + X = -8.261355821 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + X = -8.261355821 + 9.5
X = -8.261355821 + 9.5

Combine like terms: -8.261355821 + 9.5 = 1.238644179
X = 1.238644179

Simplifying
X = 1.238644179


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {17.761355821, 1.238644179}
Solution
X = {17.761355821, 1.238644179}

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