2m^2+56m+196=0

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Solution for 2m^2+56m+196=0 equation: 


Simplifying
2m2 + 56m + 196 = 0

Reorder the terms:
196 + 56m + 2m2 = 0

Solving
196 + 56m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(98 + 28m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(98 + 28m + m2)' equal to zero and attempt to solve:

Simplifying
98 + 28m + m2 = 0

Solving
98 + 28m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-98' to each side of the equation.
98 + 28m + -98 + m2 = 0 + -98

Reorder the terms:
98 + -98 + 28m + m2 = 0 + -98

Combine like terms: 98 + -98 = 0
0 + 28m + m2 = 0 + -98
28m + m2 = 0 + -98

Combine like terms: 0 + -98 = -98
28m + m2 = -98

The m term is 28m.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28m + 196 + m2 = -98 + 196

Reorder the terms:
196 + 28m + m2 = -98 + 196

Combine like terms: -98 + 196 = 98
196 + 28m + m2 = 98

Factor a perfect square on the left side:
(m + 14)(m + 14) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(m + 14) equal to 9.899494937 and -9.899494937.


Subproblem 1
m + 14 = 9.899494937

Simplifying
m + 14 = 9.899494937

Reorder the terms:
14 + m = 9.899494937

Solving
14 + m = 9.899494937

Solving for variable 'm'.

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

Add '-14' to each side of the equation.
14 + -14 + m = 9.899494937 + -14

Combine like terms: 14 + -14 = 0
0 + m = 9.899494937 + -14
m = 9.899494937 + -14

Combine like terms: 9.899494937 + -14 = -4.100505063
m = -4.100505063

Simplifying
m = -4.100505063


Subproblem 2
m + 14 = -9.899494937

Simplifying
m + 14 = -9.899494937

Reorder the terms:
14 + m = -9.899494937

Solving
14 + m = -9.899494937

Solving for variable 'm'.

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

Add '-14' to each side of the equation.
14 + -14 + m = -9.899494937 + -14

Combine like terms: 14 + -14 = 0
0 + m = -9.899494937 + -14
m = -9.899494937 + -14

Combine like terms: -9.899494937 + -14 = -23.899494937
m = -23.899494937

Simplifying
m = -23.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-4.100505063, -23.899494937}
Solution
m = {-4.100505063, -23.899494937}

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