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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 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}
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