(2x+14)*(x+4)=66

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Solution for (2x+14)*(x+4)=66 equation: 


Simplifying
(2x + 14)(x + 4) = 66

Reorder the terms:
(14 + 2x)(x + 4) = 66

Reorder the terms:
(14 + 2x)(4 + x) = 66

Multiply (14 + 2x) * (4 + x)
(14(4 + x) + 2x * (4 + x)) = 66
((4 * 14 + x * 14) + 2x * (4 + x)) = 66
((56 + 14x) + 2x * (4 + x)) = 66
(56 + 14x + (4 * 2x + x * 2x)) = 66
(56 + 14x + (8x + 2x2)) = 66

Combine like terms: 14x + 8x = 22x
(56 + 22x + 2x2) = 66

Solving
56 + 22x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
56 + -66 + 22x + 2x2 = 66 + -66

Combine like terms: 56 + -66 = -10
-10 + 22x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-10 + 22x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-5 + 11x + x2 = 0

Solving
-5 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 11x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 11x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 11x + x2 = 0 + 5
11x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
11x + x2 = 5

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 5 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 5 + 30.25

Combine like terms: 5 + 30.25 = 35.25
30.25 + 11x + x2 = 35.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.937171044 and -5.937171044.


Subproblem 1
x + 5.5 = 5.937171044

Simplifying
x + 5.5 = 5.937171044

Reorder the terms:
5.5 + x = 5.937171044

Solving
5.5 + x = 5.937171044

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 5.937171044 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.937171044 + -5.5
x = 5.937171044 + -5.5

Combine like terms: 5.937171044 + -5.5 = 0.437171044
x = 0.437171044

Simplifying
x = 0.437171044


Subproblem 2
x + 5.5 = -5.937171044

Simplifying
x + 5.5 = -5.937171044

Reorder the terms:
5.5 + x = -5.937171044

Solving
5.5 + x = -5.937171044

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -5.937171044 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.937171044 + -5.5
x = -5.937171044 + -5.5

Combine like terms: -5.937171044 + -5.5 = -11.437171044
x = -11.437171044

Simplifying
x = -11.437171044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.437171044, -11.437171044}
Solution
x = {0.437171044, -11.437171044}

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