x(64+x)=126

Solution for x(64+x)=126 equation:

Simplifying
x(64 + x) = 126
(64 * x + x * x) = 126
(64x + x2) = 126

Solving
64x + x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 64x + x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 64x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + 64x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + 64x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + 64x + x2 = 0 + 126
64x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
64x + x2 = 126

The x term is 64x.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64x + 1024 + x2 = 126 + 1024

Reorder the terms:
1024 + 64x + x2 = 126 + 1024

Combine like terms: 126 + 1024 = 1150
1024 + 64x + x2 = 1150

Factor a perfect square on the left side:
(x + 32)(x + 32) = 1150

Calculate the square root of the right side: 33.911649916

Break this problem into two subproblems by setting 
(x + 32) equal to 33.911649916 and -33.911649916.

Subproblem 1
x + 32 = 33.911649916

Simplifying
x + 32 = 33.911649916

Reorder the terms:
32 + x = 33.911649916

Solving
32 + x = 33.911649916

Solving for variable 'x'.

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

Add '-32' to each side of the equation.
32 + -32 + x = 33.911649916 + -32

Combine like terms: 32 + -32 = 0
0 + x = 33.911649916 + -32
x = 33.911649916 + -32

Combine like terms: 33.911649916 + -32 = 1.911649916
x = 1.911649916

Simplifying
x = 1.911649916

Subproblem 2
x + 32 = -33.911649916

Simplifying
x + 32 = -33.911649916

Reorder the terms:
32 + x = -33.911649916

Solving
32 + x = -33.911649916

Solving for variable 'x'.

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

Add '-32' to each side of the equation.
32 + -32 + x = -33.911649916 + -32

Combine like terms: 32 + -32 = 0
0 + x = -33.911649916 + -32
x = -33.911649916 + -32

Combine like terms: -33.911649916 + -32 = -65.911649916
x = -65.911649916

Simplifying
x = -65.911649916

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.911649916, -65.911649916}