2m^2-8m-20=0

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Solution for 2m^2-8m-20=0 equation: 


Simplifying
2m2 + -8m + -20 = 0

Reorder the terms:
-20 + -8m + 2m2 = 0

Solving
-20 + -8m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -4m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -4m + m2)' equal to zero and attempt to solve:

Simplifying
-10 + -4m + m2 = 0

Solving
-10 + -4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -4m + 10 + m2 = 0 + 10

Reorder the terms:
-10 + 10 + -4m + m2 = 0 + 10

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

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

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 = 10 + 4

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

Combine like terms: 10 + 4 = 14
4 + -4m + m2 = 14

Factor a perfect square on the left side:
(m + -2)(m + -2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(m + -2) equal to 3.741657387 and -3.741657387.


Subproblem 1
m + -2 = 3.741657387

Simplifying
m + -2 = 3.741657387

Reorder the terms:
-2 + m = 3.741657387

Solving
-2 + m = 3.741657387

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 = 3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + m = 3.741657387 + 2
m = 3.741657387 + 2

Combine like terms: 3.741657387 + 2 = 5.741657387
m = 5.741657387

Simplifying
m = 5.741657387


Subproblem 2
m + -2 = -3.741657387

Simplifying
m + -2 = -3.741657387

Reorder the terms:
-2 + m = -3.741657387

Solving
-2 + m = -3.741657387

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 = -3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + m = -3.741657387 + 2
m = -3.741657387 + 2

Combine like terms: -3.741657387 + 2 = -1.741657387
m = -1.741657387

Simplifying
m = -1.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.741657387, -1.741657387}
Solution
m = {5.741657387, -1.741657387}

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