114=(x+7)x(2)

Solution for 114=(x+7)x(2) equation:

Simplifying
114 = (x + 7) * x(2)

Reorder the terms:
114 = (7 + x) * x(2)

Reorder the terms for easier multiplication:
114 = 2x(7 + x)
114 = (7 * 2x + x * 2x)
114 = (14x + 2x2)

Solving
114 = 14x + 2x2

Solving for variable 'x'.

Reorder the terms:
114 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
114 + -14x + -2x2 = 0 + 2x2 + -2x2
114 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
114 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(57 + -7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(57 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
57 + -7x + -1x2 = 0

Solving
57 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-57 + 7x + x2 = 0

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 7x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + 7x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 7x + x2 = 0 + 57
7x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
7x + x2 = 57

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 57 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 57 + 12.25

Combine like terms: 57 + 12.25 = 69.25
12.25 + 7x + x2 = 69.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 69.25

Calculate the square root of the right side: 8.321658489

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.321658489 and -8.321658489.

Subproblem 1
x + 3.5 = 8.321658489

Simplifying
x + 3.5 = 8.321658489

Reorder the terms:
3.5 + x = 8.321658489

Solving
3.5 + x = 8.321658489

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 8.321658489 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 8.321658489 + -3.5
x = 8.321658489 + -3.5

Combine like terms: 8.321658489 + -3.5 = 4.821658489
x = 4.821658489

Simplifying
x = 4.821658489

Subproblem 2
x + 3.5 = -8.321658489

Simplifying
x + 3.5 = -8.321658489

Reorder the terms:
3.5 + x = -8.321658489

Solving
3.5 + x = -8.321658489

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -8.321658489 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -8.321658489 + -3.5
x = -8.321658489 + -3.5

Combine like terms: -8.321658489 + -3.5 = -11.821658489
x = -11.821658489

Simplifying
x = -11.821658489

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.821658489, -11.821658489}
Solution
x = {4.821658489, -11.821658489}