10m^2+22m-16=0

Solution for 10m^2+22m-16=0 equation:

Simplifying
10m2 + 22m + -16 = 0

Reorder the terms:
-16 + 22m + 10m2 = 0

Solving
-16 + 22m + 10m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 11m + 5m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 11m + 5m2)' equal to zero and attempt to solve:

Simplifying
-8 + 11m + 5m2 = 0

Solving
-8 + 11m + 5m2 = 0

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

Divide each side by '5'.
-1.6 + 2.2m + m2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2.2m + 1.6 + m2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2.2m + m2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2.2m + m2 = 0 + 1.6
2.2m + m2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2.2m + m2 = 1.6

The m term is 2.2m.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2m + 1.21 + m2 = 1.6 + 1.21

Reorder the terms:
1.21 + 2.2m + m2 = 1.6 + 1.21

Combine like terms: 1.6 + 1.21 = 2.81
1.21 + 2.2m + m2 = 2.81

Factor a perfect square on the left side:
(m + 1.1)(m + 1.1) = 2.81

Calculate the square root of the right side: 1.676305461

Break this problem into two subproblems by setting 
(m + 1.1) equal to 1.676305461 and -1.676305461.

Subproblem 1
m + 1.1 = 1.676305461

Simplifying
m + 1.1 = 1.676305461

Reorder the terms:
1.1 + m = 1.676305461

Solving
1.1 + m = 1.676305461

Solving for variable 'm'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + m = 1.676305461 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + m = 1.676305461 + -1.1
m = 1.676305461 + -1.1

Combine like terms: 1.676305461 + -1.1 = 0.576305461
m = 0.576305461

Simplifying
m = 0.576305461

Subproblem 2
m + 1.1 = -1.676305461

Simplifying
m + 1.1 = -1.676305461

Reorder the terms:
1.1 + m = -1.676305461

Solving
1.1 + m = -1.676305461

Solving for variable 'm'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + m = -1.676305461 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + m = -1.676305461 + -1.1
m = -1.676305461 + -1.1

Combine like terms: -1.676305461 + -1.1 = -2.776305461
m = -2.776305461

Simplifying
m = -2.776305461

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.576305461, -2.776305461}
Solution
m = {0.576305461, -2.776305461}