x^2+4x-42=0

Solution for x^2+4x-42=0 equation:

Simplifying
x2 + 4x + -42 = 0

Reorder the terms:
-42 + 4x + x2 = 0

Solving
-42 + 4x + 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 + 4x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 4x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 4x + x2 = 0 + 42
4x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
4x + x2 = 42

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 42 + 4

Reorder the terms:
4 + 4x + x2 = 42 + 4

Combine like terms: 42 + 4 = 46
4 + 4x + x2 = 46

Factor a perfect square on the left side:
(x + 2)(x + 2) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 2) equal to 6.782329983 and -6.782329983.

Subproblem 1
x + 2 = 6.782329983

Simplifying
x + 2 = 6.782329983

Reorder the terms:
2 + x = 6.782329983

Solving
2 + x = 6.782329983

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.782329983 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.782329983 + -2
x = 6.782329983 + -2

Combine like terms: 6.782329983 + -2 = 4.782329983
x = 4.782329983

Simplifying
x = 4.782329983

Subproblem 2
x + 2 = -6.782329983

Simplifying
x + 2 = -6.782329983

Reorder the terms:
2 + x = -6.782329983

Solving
2 + x = -6.782329983

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.782329983 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.782329983 + -2
x = -6.782329983 + -2

Combine like terms: -6.782329983 + -2 = -8.782329983
x = -8.782329983

Simplifying
x = -8.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.782329983, -8.782329983}