10m^2-2m-7=0

Solution for 10m^2-2m-7=0 equation:

Simplifying
10m2 + -2m + -7 = 0

Reorder the terms:
-7 + -2m + 10m2 = 0

Solving
-7 + -2m + 10m2 = 0

Solving for variable 'm'.

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

Divide each side by '10'.
-0.7 + -0.2m + m2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + -0.2m + 0.7 + m2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + -0.2m + m2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + -0.2m + m2 = 0 + 0.7
-0.2m + m2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
-0.2m + m2 = 0.7

The m term is -0.2m.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2m + 0.01 + m2 = 0.7 + 0.01

Reorder the terms:
0.01 + -0.2m + m2 = 0.7 + 0.01

Combine like terms: 0.7 + 0.01 = 0.71
0.01 + -0.2m + m2 = 0.71

Factor a perfect square on the left side:
(m + -0.1)(m + -0.1) = 0.71

Calculate the square root of the right side: 0.842614977

Break this problem into two subproblems by setting 
(m + -0.1) equal to 0.842614977 and -0.842614977.

Subproblem 1
m + -0.1 = 0.842614977

Simplifying
m + -0.1 = 0.842614977

Reorder the terms:
-0.1 + m = 0.842614977

Solving
-0.1 + m = 0.842614977

Solving for variable 'm'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + m = 0.842614977 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + m = 0.842614977 + 0.1
m = 0.842614977 + 0.1

Combine like terms: 0.842614977 + 0.1 = 0.942614977
m = 0.942614977

Simplifying
m = 0.942614977

Subproblem 2
m + -0.1 = -0.842614977

Simplifying
m + -0.1 = -0.842614977

Reorder the terms:
-0.1 + m = -0.842614977

Solving
-0.1 + m = -0.842614977

Solving for variable 'm'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + m = -0.842614977 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + m = -0.842614977 + 0.1
m = -0.842614977 + 0.1

Combine like terms: -0.842614977 + 0.1 = -0.742614977
m = -0.742614977

Simplifying
m = -0.742614977

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.942614977, -0.742614977}