u^2+16u+42=0

Solution for u^2+16u+42=0 equation:

Simplifying
u2 + 16u + 42 = 0

Reorder the terms:
42 + 16u + u2 = 0

Solving
42 + 16u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 16u + -42 + u2 = 0 + -42

Reorder the terms:
42 + -42 + 16u + u2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 16u + u2 = 0 + -42
16u + u2 = 0 + -42

Combine like terms: 0 + -42 = -42
16u + u2 = -42

The u term is 16u.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16u + 64 + u2 = -42 + 64

Reorder the terms:
64 + 16u + u2 = -42 + 64

Combine like terms: -42 + 64 = 22
64 + 16u + u2 = 22

Factor a perfect square on the left side:
(u + 8)(u + 8) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(u + 8) equal to 4.69041576 and -4.69041576.

Subproblem 1
u + 8 = 4.69041576

Simplifying
u + 8 = 4.69041576

Reorder the terms:
8 + u = 4.69041576

Solving
8 + u = 4.69041576

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = 4.69041576 + -8

Combine like terms: 8 + -8 = 0
0 + u = 4.69041576 + -8
u = 4.69041576 + -8

Combine like terms: 4.69041576 + -8 = -3.30958424
u = -3.30958424

Simplifying
u = -3.30958424

Subproblem 2
u + 8 = -4.69041576

Simplifying
u + 8 = -4.69041576

Reorder the terms:
8 + u = -4.69041576

Solving
8 + u = -4.69041576

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = -4.69041576 + -8

Combine like terms: 8 + -8 = 0
0 + u = -4.69041576 + -8
u = -4.69041576 + -8

Combine like terms: -4.69041576 + -8 = -12.69041576
u = -12.69041576

Simplifying
u = -12.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-3.30958424, -12.69041576}