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```Simplifying
m2 + -4m + -21 = 0

Reorder the terms:
-21 + -4m + m2 = 0

Solving
-21 + -4m + m2 = 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 + m2 = 0 + 21

Reorder the terms:
-21 + 21 + -4m + m2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4m + m2 = 0 + 21
-4m + m2 = 0 + 21

Combine like terms: 0 + 21 = 21
-4m + m2 = 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 + m2 = 21 + 4

Reorder the terms:
4 + -4m + m2 = 21 + 4

Combine like terms: 21 + 4 = 25
4 + -4m + m2 = 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 1m + -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 2m + -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

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