X(4X+8)=28

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Solution for X(4X+8)=28 equation: 


Simplifying
X(4X + 8) = 28

Reorder the terms:
X(8 + 4X) = 28
(8 * X + 4X * X) = 28
(8X + 4X2) = 28

Solving
8X + 4X2 = 28

Solving for variable 'X'.

Reorder the terms:
-28 + 8X + 4X2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 8X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 2X + X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + 2X + X2)' equal to zero and attempt to solve:

Simplifying
-7 + 2X + X2 = 0

Solving
-7 + 2X + X2 = 0

Begin completing the square.

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 = 1.828427125
X = 1.828427125

Simplifying
X = 1.828427125


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 = -3.828427125
X = -3.828427125

Simplifying
X = -3.828427125


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

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