2m^2-4m+8=10

Solution for 2m^2-4m+8=10 equation:

Simplifying
2m2 + -4m + 8 = 10

Reorder the terms:
8 + -4m + 2m2 = 10

Solving
8 + -4m + 2m2 = 10

Solving for variable 'm'.

Reorder the terms:
8 + -10 + -4m + 2m2 = 10 + -10

Combine like terms: 8 + -10 = -2
-2 + -4m + 2m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-2 + -4m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2m + m2) = 0

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

Simplifying
-1 + -2m + m2 = 0

Solving
-1 + -2m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -2m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2m + m2 = 0 + 1
-2m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2m + m2 = 1

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 1 + 1

Reorder the terms:
1 + -2m + m2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2m + m2 = 2

Factor a perfect square on the left side:
(m + -1)(m + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(m + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
m + -1 = 1.414213562

Simplifying
m + -1 = 1.414213562

Reorder the terms:
-1 + m = 1.414213562

Solving
-1 + m = 1.414213562

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + m = 1.414213562 + 1
m = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
m = 2.414213562

Simplifying
m = 2.414213562

Subproblem 2
m + -1 = -1.414213562

Simplifying
m + -1 = -1.414213562

Reorder the terms:
-1 + m = -1.414213562

Solving
-1 + m = -1.414213562

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + m = -1.414213562 + 1
m = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
m = -0.414213562

Simplifying
m = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.414213562, -0.414213562}
Solution
m = {2.414213562, -0.414213562}