(2x)(x+2)=52

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Solution for (2x)(x+2)=52 equation: 


Simplifying
(2x)(x + 2) = 52

Remove parenthesis around (2x)
2x(x + 2) = 52

Reorder the terms:
2x(2 + x) = 52
(2 * 2x + x * 2x) = 52
(4x + 2x2) = 52

Solving
4x + 2x2 = 52

Solving for variable 'x'.

Reorder the terms:
-52 + 4x + 2x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-26 + 2x + x2 = 0

Solving
-26 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 2x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2x + x2 = 0 + 26
2x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
2x + x2 = 26

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 = 26 + 1

Reorder the terms:
1 + 2x + x2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + 2x + x2 = 27

Factor a perfect square on the left side:
(x + 1)(x + 1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 1) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + 1 = 5.196152423

Simplifying
x + 1 = 5.196152423

Reorder the terms:
1 + x = 5.196152423

Solving
1 + x = 5.196152423

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 = 5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.196152423 + -1
x = 5.196152423 + -1

Combine like terms: 5.196152423 + -1 = 4.196152423
x = 4.196152423

Simplifying
x = 4.196152423


Subproblem 2
x + 1 = -5.196152423

Simplifying
x + 1 = -5.196152423

Reorder the terms:
1 + x = -5.196152423

Solving
1 + x = -5.196152423

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 = -5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.196152423 + -1
x = -5.196152423 + -1

Combine like terms: -5.196152423 + -1 = -6.196152423
x = -6.196152423

Simplifying
x = -6.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.196152423, -6.196152423}
Solution
x = {4.196152423, -6.196152423}

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