4x(x-6)=22

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Solution for 4x(x-6)=22 equation: 


Simplifying
4x(x + -6) = 22

Reorder the terms:
4x(-6 + x) = 22
(-6 * 4x + x * 4x) = 22
(-24x + 4x2) = 22

Solving
-24x + 4x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + -24x + 4x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -12x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -12x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + -12x + 2x2 = 0

Solving
-11 + -12x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -6x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -6x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -6x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -6x + x2 = 0 + 5.5
-6x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-6x + x2 = 5.5

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 = 5.5 + 9

Reorder the terms:
9 + -6x + x2 = 5.5 + 9

Combine like terms: 5.5 + 9 = 14.5
9 + -6x + x2 = 14.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(x + -3) equal to 3.807886553 and -3.807886553.


Subproblem 1
x + -3 = 3.807886553

Simplifying
x + -3 = 3.807886553

Reorder the terms:
-3 + x = 3.807886553

Solving
-3 + x = 3.807886553

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 = 3.807886553 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.807886553 + 3
x = 3.807886553 + 3

Combine like terms: 3.807886553 + 3 = 6.807886553
x = 6.807886553

Simplifying
x = 6.807886553


Subproblem 2
x + -3 = -3.807886553

Simplifying
x + -3 = -3.807886553

Reorder the terms:
-3 + x = -3.807886553

Solving
-3 + x = -3.807886553

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 = -3.807886553 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.807886553 + 3
x = -3.807886553 + 3

Combine like terms: -3.807886553 + 3 = -0.807886553
x = -0.807886553

Simplifying
x = -0.807886553


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.807886553, -0.807886553}
Solution
x = {6.807886553, -0.807886553}

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