3X(X+2)=8

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Solution for 3X(X+2)=8 equation: 


Simplifying
3X(X + 2) = 8

Reorder the terms:
3X(2 + X) = 8
(2 * 3X + X * 3X) = 8
(6X + 3X2) = 8

Solving
6X + 3X2 = 8

Solving for variable 'X'.

Reorder the terms:
-8 + 6X + 3X2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 6X + 3X2 = 0

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

Divide each side by '3'.
-2.666666667 + 2X + X2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 2X + 2.666666667 + X2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 2X + X2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 2X + X2 = 0 + 2.666666667
2X + X2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
2X + X2 = 2.666666667

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 = 2.666666667 + 1

Reorder the terms:
1 + 2X + X2 = 2.666666667 + 1

Combine like terms: 2.666666667 + 1 = 3.666666667
1 + 2X + X2 = 3.666666667

Factor a perfect square on the left side:
(X + 1)(X + 1) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(X + 1) equal to 1.914854216 and -1.914854216.


Subproblem 1
X + 1 = 1.914854216

Simplifying
X + 1 = 1.914854216

Reorder the terms:
1 + X = 1.914854216

Solving
1 + X = 1.914854216

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 = 1.914854216 + -1

Combine like terms: 1 + -1 = 0
0 + X = 1.914854216 + -1
X = 1.914854216 + -1

Combine like terms: 1.914854216 + -1 = 0.914854216
X = 0.914854216

Simplifying
X = 0.914854216


Subproblem 2
X + 1 = -1.914854216

Simplifying
X + 1 = -1.914854216

Reorder the terms:
1 + X = -1.914854216

Solving
1 + X = -1.914854216

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 = -1.914854216 + -1

Combine like terms: 1 + -1 = 0
0 + X = -1.914854216 + -1
X = -1.914854216 + -1

Combine like terms: -1.914854216 + -1 = -2.914854216
X = -2.914854216

Simplifying
X = -2.914854216


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.914854216, -2.914854216}

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