2x+22=4x(x+3)

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Solution for 2x+22=4x(x+3) equation: 


Simplifying
2x + 22 = 4x(x + 3)

Reorder the terms:
22 + 2x = 4x(x + 3)

Reorder the terms:
22 + 2x = 4x(3 + x)
22 + 2x = (3 * 4x + x * 4x)
22 + 2x = (12x + 4x2)

Solving
22 + 2x = 12x + 4x2

Solving for variable 'x'.

Combine like terms: 2x + -12x = -10x
22 + -10x + -4x2 = 12x + 4x2 + -12x + -4x2

Reorder the terms:
22 + -10x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
22 + -10x + -4x2 = 0 + 4x2 + -4x2
22 + -10x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
22 + -10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -5x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -5x + -2x2)' equal to zero and attempt to solve:

Simplifying
11 + -5x + -2x2 = 0

Solving
11 + -5x + -2x2 = 0

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

Divide each side by '-2'.
-5.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 2.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 2.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 2.5x + x2 = 0 + 5.5
2.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
2.5x + x2 = 5.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 5.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 5.5 + 1.5625

Combine like terms: 5.5 + 1.5625 = 7.0625
1.5625 + 2.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.657536453 and -2.657536453.


Subproblem 1
x + 1.25 = 2.657536453

Simplifying
x + 1.25 = 2.657536453

Reorder the terms:
1.25 + x = 2.657536453

Solving
1.25 + x = 2.657536453

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.657536453 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.657536453 + -1.25
x = 2.657536453 + -1.25

Combine like terms: 2.657536453 + -1.25 = 1.407536453
x = 1.407536453

Simplifying
x = 1.407536453


Subproblem 2
x + 1.25 = -2.657536453

Simplifying
x + 1.25 = -2.657536453

Reorder the terms:
1.25 + x = -2.657536453

Solving
1.25 + x = -2.657536453

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.657536453 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.657536453 + -1.25
x = -2.657536453 + -1.25

Combine like terms: -2.657536453 + -1.25 = -3.907536453
x = -3.907536453

Simplifying
x = -3.907536453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.407536453, -3.907536453}
Solution
x = {1.407536453, -3.907536453}

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