m^2+2m-42=0

Solution for m^2+2m-42=0 equation:

Simplifying
m2 + 2m + -42 = 0

Reorder the terms:
-42 + 2m + m2 = 0

Solving
-42 + 2m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 2m + 42 + m2 = 0 + 42

Reorder the terms:
-42 + 42 + 2m + m2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 2m + m2 = 0 + 42
2m + m2 = 0 + 42

Combine like terms: 0 + 42 = 42
2m + m2 = 42

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = 42 + 1

Reorder the terms:
1 + 2m + m2 = 42 + 1

Combine like terms: 42 + 1 = 43
1 + 2m + m2 = 43

Factor a perfect square on the left side:
(m + 1)(m + 1) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(m + 1) equal to 6.557438524 and -6.557438524.

Subproblem 1
m + 1 = 6.557438524

Simplifying
m + 1 = 6.557438524

Reorder the terms:
1 + m = 6.557438524

Solving
1 + m = 6.557438524

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 6.557438524 + -1

Combine like terms: 1 + -1 = 0
0 + m = 6.557438524 + -1
m = 6.557438524 + -1

Combine like terms: 6.557438524 + -1 = 5.557438524
m = 5.557438524

Simplifying
m = 5.557438524

Subproblem 2
m + 1 = -6.557438524

Simplifying
m + 1 = -6.557438524

Reorder the terms:
1 + m = -6.557438524

Solving
1 + m = -6.557438524

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -6.557438524 + -1

Combine like terms: 1 + -1 = 0
0 + m = -6.557438524 + -1
m = -6.557438524 + -1

Combine like terms: -6.557438524 + -1 = -7.557438524
m = -7.557438524

Simplifying
m = -7.557438524

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.557438524, -7.557438524}