10m^2-12m-21=-2

Solution for 10m^2-12m-21=-2 equation:

Simplifying
10m2 + -12m + -21 = -2

Reorder the terms:
-21 + -12m + 10m2 = -2

Solving
-21 + -12m + 10m2 = -2

Solving for variable 'm'.

Reorder the terms:
-21 + 2 + -12m + 10m2 = -2 + 2

Combine like terms: -21 + 2 = -19
-19 + -12m + 10m2 = -2 + 2

Combine like terms: -2 + 2 = 0
-19 + -12m + 10m2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-1.9 + -1.2m + m2 = 0

Move the constant term to the right:

Add '1.9' to each side of the equation.
-1.9 + -1.2m + 1.9 + m2 = 0 + 1.9

Reorder the terms:
-1.9 + 1.9 + -1.2m + m2 = 0 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + -1.2m + m2 = 0 + 1.9
-1.2m + m2 = 0 + 1.9

Combine like terms: 0 + 1.9 = 1.9
-1.2m + m2 = 1.9

The m term is -1.2m.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2m + 0.36 + m2 = 1.9 + 0.36

Reorder the terms:
0.36 + -1.2m + m2 = 1.9 + 0.36

Combine like terms: 1.9 + 0.36 = 2.26
0.36 + -1.2m + m2 = 2.26

Factor a perfect square on the left side:
(m + -0.6)(m + -0.6) = 2.26

Calculate the square root of the right side: 1.503329638

Break this problem into two subproblems by setting 
(m + -0.6) equal to 1.503329638 and -1.503329638.

Subproblem 1
m + -0.6 = 1.503329638

Simplifying
m + -0.6 = 1.503329638

Reorder the terms:
-0.6 + m = 1.503329638

Solving
-0.6 + m = 1.503329638

Solving for variable 'm'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + m = 1.503329638 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + m = 1.503329638 + 0.6
m = 1.503329638 + 0.6

Combine like terms: 1.503329638 + 0.6 = 2.103329638
m = 2.103329638

Simplifying
m = 2.103329638

Subproblem 2
m + -0.6 = -1.503329638

Simplifying
m + -0.6 = -1.503329638

Reorder the terms:
-0.6 + m = -1.503329638

Solving
-0.6 + m = -1.503329638

Solving for variable 'm'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + m = -1.503329638 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + m = -1.503329638 + 0.6
m = -1.503329638 + 0.6

Combine like terms: -1.503329638 + 0.6 = -0.903329638
m = -0.903329638

Simplifying
m = -0.903329638

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.103329638, -0.903329638}