x(2x+8)=28

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Solution for x(2x+8)=28 equation: 


Simplifying
x(2x + 8) = 28

Reorder the terms:
x(8 + 2x) = 28
(8 * x + 2x * x) = 28
(8x + 2x2) = 28

Solving
8x + 2x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + 8x + 2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + 4x + x2 = 0

Solving
-14 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 4x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 4x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 4x + x2 = 0 + 14
4x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
4x + x2 = 14

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 14 + 4

Reorder the terms:
4 + 4x + x2 = 14 + 4

Combine like terms: 14 + 4 = 18
4 + 4x + x2 = 18

Factor a perfect square on the left side:
(x + 2)(x + 2) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 2) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 2 = 4.242640687

Simplifying
x + 2 = 4.242640687

Reorder the terms:
2 + x = 4.242640687

Solving
2 + x = 4.242640687

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.242640687 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.242640687 + -2
x = 4.242640687 + -2

Combine like terms: 4.242640687 + -2 = 2.242640687
x = 2.242640687

Simplifying
x = 2.242640687


Subproblem 2
x + 2 = -4.242640687

Simplifying
x + 2 = -4.242640687

Reorder the terms:
2 + x = -4.242640687

Solving
2 + x = -4.242640687

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.242640687 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.242640687 + -2
x = -4.242640687 + -2

Combine like terms: -4.242640687 + -2 = -6.242640687
x = -6.242640687

Simplifying
x = -6.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.242640687, -6.242640687}
Solution
x = {2.242640687, -6.242640687}

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