x(2x+6)=228

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Solution for x(2x+6)=228 equation: 


Simplifying
x(2x + 6) = 228

Reorder the terms:
x(6 + 2x) = 228
(6 * x + 2x * x) = 228
(6x + 2x2) = 228

Solving
6x + 2x2 = 228

Solving for variable 'x'.

Reorder the terms:
-228 + 6x + 2x2 = 228 + -228

Combine like terms: 228 + -228 = 0
-228 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-114 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-114 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-114 + 3x + x2 = 0

Solving
-114 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 3x + 114 + x2 = 0 + 114

Reorder the terms:
-114 + 114 + 3x + x2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 3x + x2 = 0 + 114
3x + x2 = 0 + 114

Combine like terms: 0 + 114 = 114
3x + x2 = 114

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 114 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 114 + 2.25

Combine like terms: 114 + 2.25 = 116.25
2.25 + 3x + x2 = 116.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(x + 1.5) equal to 10.781929326 and -10.781929326.


Subproblem 1
x + 1.5 = 10.781929326

Simplifying
x + 1.5 = 10.781929326

Reorder the terms:
1.5 + x = 10.781929326

Solving
1.5 + x = 10.781929326

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 10.781929326 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 10.781929326 + -1.5
x = 10.781929326 + -1.5

Combine like terms: 10.781929326 + -1.5 = 9.281929326
x = 9.281929326

Simplifying
x = 9.281929326


Subproblem 2
x + 1.5 = -10.781929326

Simplifying
x + 1.5 = -10.781929326

Reorder the terms:
1.5 + x = -10.781929326

Solving
1.5 + x = -10.781929326

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -10.781929326 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -10.781929326 + -1.5
x = -10.781929326 + -1.5

Combine like terms: -10.781929326 + -1.5 = -12.281929326
x = -12.281929326

Simplifying
x = -12.281929326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.281929326, -12.281929326}
Solution
x = {9.281929326, -12.281929326}

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