x=x^2+64x+4

Solution for x=x^2+64x+4 equation:

Simplifying
x = x2 + 64x + 4

Reorder the terms:
x = 4 + 64x + x2

Solving
x = 4 + 64x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + x + -64x + -1x2 = 4 + 64x + x2 + -4 + -64x + -1x2

Combine like terms: x + -64x = -63x
-4 + -63x + -1x2 = 4 + 64x + x2 + -4 + -64x + -1x2

Reorder the terms:
-4 + -63x + -1x2 = 4 + -4 + 64x + -64x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + -63x + -1x2 = 0 + 64x + -64x + x2 + -1x2
-4 + -63x + -1x2 = 64x + -64x + x2 + -1x2

Combine like terms: 64x + -64x = 0
-4 + -63x + -1x2 = 0 + x2 + -1x2
-4 + -63x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -63x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 63x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 63x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 63x + x2 = 0

Solving
4 + 63x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 63x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 63x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 63x + x2 = 0 + -4
63x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
63x + x2 = -4

The x term is 63x.  Take half its coefficient (31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
63x + 992.25 + x2 = -4 + 992.25

Reorder the terms:
992.25 + 63x + x2 = -4 + 992.25

Combine like terms: -4 + 992.25 = 988.25
992.25 + 63x + x2 = 988.25

Factor a perfect square on the left side:
(x + 31.5)(x + 31.5) = 988.25

Calculate the square root of the right side: 31.436443819

Break this problem into two subproblems by setting 
(x + 31.5) equal to 31.436443819 and -31.436443819.

Subproblem 1
x + 31.5 = 31.436443819

Simplifying
x + 31.5 = 31.436443819

Reorder the terms:
31.5 + x = 31.436443819

Solving
31.5 + x = 31.436443819

Solving for variable 'x'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + x = 31.436443819 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + x = 31.436443819 + -31.5
x = 31.436443819 + -31.5

Combine like terms: 31.436443819 + -31.5 = -0.063556181
x = -0.063556181

Simplifying
x = -0.063556181

Subproblem 2
x + 31.5 = -31.436443819

Simplifying
x + 31.5 = -31.436443819

Reorder the terms:
31.5 + x = -31.436443819

Solving
31.5 + x = -31.436443819

Solving for variable 'x'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + x = -31.436443819 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + x = -31.436443819 + -31.5
x = -31.436443819 + -31.5

Combine like terms: -31.436443819 + -31.5 = -62.936443819
x = -62.936443819

Simplifying
x = -62.936443819

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.063556181, -62.936443819}
Solution
x = {-0.063556181, -62.936443819}