2x^2+16x+42=x^2

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

Simplifying
2x2 + 16x + 42 = x2

Reorder the terms:
42 + 16x + 2x2 = x2

Solving
42 + 16x + 2x2 = x2

Solving for variable 'x'.

Combine like terms: 2x2 + -1x2 = 1x2
42 + 16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 16x + 1x2 = 0

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 = 22
64 + 16x + x2 = 22

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

Calculate the square root of the right side: 4.69041576

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

Subproblem 1
x + 8 = 4.69041576

Simplifying
x + 8 = 4.69041576

Reorder the terms:
8 + x = 4.69041576

Solving
8 + x = 4.69041576

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 = 4.69041576 + -8

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

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

Simplifying
x = -3.30958424

Subproblem 2
x + 8 = -4.69041576

Simplifying
x + 8 = -4.69041576

Reorder the terms:
8 + x = -4.69041576

Solving
8 + x = -4.69041576

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 = -4.69041576 + -8

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

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

Simplifying
x = -12.69041576

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