x=x(x+14)+54

Solution for x=x(x+14)+54 equation:

Simplifying
x = x(x + 14) + 54

Reorder the terms:
x = x(14 + x) + 54
x = (14 * x + x * x) + 54
x = (14x + x2) + 54

Reorder the terms:
x = 54 + 14x + x2

Solving
x = 54 + 14x + x2

Solving for variable 'x'.

Reorder the terms:
-54 + x + -14x + -1x2 = 54 + 14x + x2 + -54 + -14x + -1x2

Combine like terms: x + -14x = -13x
-54 + -13x + -1x2 = 54 + 14x + x2 + -54 + -14x + -1x2

Reorder the terms:
-54 + -13x + -1x2 = 54 + -54 + 14x + -14x + x2 + -1x2

Combine like terms: 54 + -54 = 0
-54 + -13x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-54 + -13x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-54 + -13x + -1x2 = 0 + x2 + -1x2
-54 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-54 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(54 + 13x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(54 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
54 + 13x + x2 = 0

Solving
54 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + 13x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + 13x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 13x + x2 = 0 + -54
13x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
13x + x2 = -54

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -54 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -54 + 42.25

Combine like terms: -54 + 42.25 = -11.75
42.25 + 13x + x2 = -11.75

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = -11.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.