x^2+68x=32

Solution for x^2+68x=32 equation:

Simplifying
x2 + 68x = 32

Reorder the terms:
68x + x2 = 32

Solving
68x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 68x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 68x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 68x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 68x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 68x + x2 = 0 + 32
68x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
68x + x2 = 32

The x term is 68x.  Take half its coefficient (34).
Square it (1156) and add it to both sides.

Add '1156' to each side of the equation.
68x + 1156 + x2 = 32 + 1156

Reorder the terms:
1156 + 68x + x2 = 32 + 1156

Combine like terms: 32 + 1156 = 1188
1156 + 68x + x2 = 1188

Factor a perfect square on the left side:
(x + 34)(x + 34) = 1188

Calculate the square root of the right side: 34.467375879

Break this problem into two subproblems by setting 
(x + 34) equal to 34.467375879 and -34.467375879.

Subproblem 1
x + 34 = 34.467375879

Simplifying
x + 34 = 34.467375879

Reorder the terms:
34 + x = 34.467375879

Solving
34 + x = 34.467375879

Solving for variable 'x'.

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

Add '-34' to each side of the equation.
34 + -34 + x = 34.467375879 + -34

Combine like terms: 34 + -34 = 0
0 + x = 34.467375879 + -34
x = 34.467375879 + -34

Combine like terms: 34.467375879 + -34 = 0.467375879
x = 0.467375879

Simplifying
x = 0.467375879

Subproblem 2
x + 34 = -34.467375879

Simplifying
x + 34 = -34.467375879

Reorder the terms:
34 + x = -34.467375879

Solving
34 + x = -34.467375879

Solving for variable 'x'.

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

Add '-34' to each side of the equation.
34 + -34 + x = -34.467375879 + -34

Combine like terms: 34 + -34 = 0
0 + x = -34.467375879 + -34
x = -34.467375879 + -34

Combine like terms: -34.467375879 + -34 = -68.467375879
x = -68.467375879

Simplifying
x = -68.467375879

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.467375879, -68.467375879}