Simplifying
m^{2} + -4m + -21 = 0
Reorder the terms:
-21 + -4m + m^{2} = 0
Solving
-21 + -4m + m^{2} = 0
Solving for variable 'm'.
Begin completing the square.
Move the constant term to the right:
Add '21' to each side of the equation.
-21 + -4m + 21 + m^{2} = 0 + 21
Reorder the terms:
-21 + 21 + -4m + m^{2} = 0 + 21
Combine like terms: -21 + 21 = 0
0 + -4m + m^{2} = 0 + 21
-4m + m^{2} = 0 + 21
Combine like terms: 0 + 21 = 21
-4m + m^{2} = 21
The m term is -4m. Take half its coefficient (-2).
Square it (4) and add it to both sides.
Add '4' to each side of the equation.
-4m + 4 + m^{2} = 21 + 4
Reorder the terms:
4 + -4m + m^{2} = 21 + 4
Combine like terms: 21 + 4 = 25
4 + -4m + m^{2} = 25
Factor a perfect square on the left side:
(m + -2)(m + -2) = 25
Calculate the square root of the right side: 5
Break this problem into two subproblems by setting
(m + -2) equal to 5 and -5.
#### Subproblem 1

m + -2 = 5
Simplifying
m + -2 = 5
Reorder the terms:
-2 + m = 5
Solving
-2 + m = 5
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + m = 5 + 2
Combine like terms: -2 + 2 = 0
0 + m = 5 + 2
m = 5 + 2
Combine like terms: 5 + 2 = 7
m = 7
Simplifying
m = 7
#### Subproblem 2

m + -2 = -5
Simplifying
m + -2 = -5
Reorder the terms:
-2 + m = -5
Solving
-2 + m = -5
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + m = -5 + 2
Combine like terms: -2 + 2 = 0
0 + m = -5 + 2
m = -5 + 2
Combine like terms: -5 + 2 = -3
m = -3
Simplifying
m = -3
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
m = {7, -3}