6+4(x+2)=2x^2

Solution for 6+4(x+2)=2x^2 equation:

Simplifying
6 + 4(x + 2) = 2x2

Reorder the terms:
6 + 4(2 + x) = 2x2
6 + (2 * 4 + x * 4) = 2x2
6 + (8 + 4x) = 2x2

Combine like terms: 6 + 8 = 14
14 + 4x = 2x2

Solving
14 + 4x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
14 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + 2x + -1x2 = 0

Solving
7 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-7 + -2x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -2x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x + x2 = 0 + 7
-2x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2x + x2 = 7

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 7 + 1

Reorder the terms:
1 + -2x + x2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2x + x2 = 8

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1
x + -1 = 2.828427125

Simplifying
x + -1 = 2.828427125

Reorder the terms:
-1 + x = 2.828427125

Solving
-1 + x = 2.828427125

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.828427125 + 1
x = 2.828427125 + 1

Combine like terms: 2.828427125 + 1 = 3.828427125
x = 3.828427125

Simplifying
x = 3.828427125

Subproblem 2
x + -1 = -2.828427125

Simplifying
x + -1 = -2.828427125

Reorder the terms:
-1 + x = -2.828427125

Solving
-1 + x = -2.828427125

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.828427125 + 1
x = -2.828427125 + 1

Combine like terms: -2.828427125 + 1 = -1.828427125
x = -1.828427125

Simplifying
x = -1.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.828427125, -1.828427125}
Solution
x = {3.828427125, -1.828427125}