2(2x^2+11x-228)=0

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Solution for 2(2x^2+11x-228)=0 equation: 


Simplifying
2(2x2 + 11x + -228) = 0

Reorder the terms:
2(-228 + 11x + 2x2) = 0
(-228 * 2 + 11x * 2 + 2x2 * 2) = 0
(-456 + 22x + 4x2) = 0

Solving
-456 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-228 + 11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-228 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-228 + 11x + 2x2 = 0

Solving
-228 + 11x + 2x2 = 0

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

Divide each side by '2'.
-114 + 5.5x + x2 = 0

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 5.5x + 114 + x2 = 0 + 114

Reorder the terms:
-114 + 114 + 5.5x + x2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 5.5x + x2 = 0 + 114
5.5x + x2 = 0 + 114

Combine like terms: 0 + 114 = 114
5.5x + x2 = 114

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 114 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 114 + 7.5625

Combine like terms: 114 + 7.5625 = 121.5625
7.5625 + 5.5x + x2 = 121.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 121.5625

Calculate the square root of the right side: 11.025538536

Break this problem into two subproblems by setting 
(x + 2.75) equal to 11.025538536 and -11.025538536.


Subproblem 1
x + 2.75 = 11.025538536

Simplifying
x + 2.75 = 11.025538536

Reorder the terms:
2.75 + x = 11.025538536

Solving
2.75 + x = 11.025538536

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 11.025538536 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 11.025538536 + -2.75
x = 11.025538536 + -2.75

Combine like terms: 11.025538536 + -2.75 = 8.275538536
x = 8.275538536

Simplifying
x = 8.275538536


Subproblem 2
x + 2.75 = -11.025538536

Simplifying
x + 2.75 = -11.025538536

Reorder the terms:
2.75 + x = -11.025538536

Solving
2.75 + x = -11.025538536

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -11.025538536 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -11.025538536 + -2.75
x = -11.025538536 + -2.75

Combine like terms: -11.025538536 + -2.75 = -13.775538536
x = -13.775538536

Simplifying
x = -13.775538536


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.275538536, -13.775538536}
Solution
x = {8.275538536, -13.775538536}

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