x^2+16x-42=0

Solution for x^2+16x-42=0 equation:

Simplifying
x2 + 16x + -42 = 0

Reorder the terms:
-42 + 16x + x2 = 0

Solving
-42 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 16x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 16x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 16x + x2 = 0 + 42
16x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
16x + x2 = 42

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

Add '64' to each side of the equation.
16x + 64 + x2 = 42 + 64

Reorder the terms:
64 + 16x + x2 = 42 + 64

Combine like terms: 42 + 64 = 106
64 + 16x + x2 = 106

Factor a perfect square on the left side:
(x + 8)(x + 8) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 8) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + 8 = 10.295630141

Simplifying
x + 8 = 10.295630141

Reorder the terms:
8 + x = 10.295630141

Solving
8 + x = 10.295630141

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 10.295630141 + -8

Combine like terms: 8 + -8 = 0
0 + x = 10.295630141 + -8
x = 10.295630141 + -8

Combine like terms: 10.295630141 + -8 = 2.295630141
x = 2.295630141

Simplifying
x = 2.295630141

Subproblem 2
x + 8 = -10.295630141

Simplifying
x + 8 = -10.295630141

Reorder the terms:
8 + x = -10.295630141

Solving
8 + x = -10.295630141

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -10.295630141 + -8

Combine like terms: 8 + -8 = 0
0 + x = -10.295630141 + -8
x = -10.295630141 + -8

Combine like terms: -10.295630141 + -8 = -18.295630141
x = -18.295630141

Simplifying
x = -18.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.295630141, -18.295630141}