4m^2-2m-48=0

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Solution for 4m^2-2m-48=0 equation: 


Simplifying
4m2 + -2m + -48 = 0

Reorder the terms:
-48 + -2m + 4m2 = 0

Solving
-48 + -2m + 4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -1m + 2m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + -1m + 2m2)' equal to zero and attempt to solve:

Simplifying
-24 + -1m + 2m2 = 0

Solving
-24 + -1m + 2m2 = 0

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

Divide each side by '2'.
-12 + -0.5m + m2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -0.5m + 12 + m2 = 0 + 12

Reorder the terms:
-12 + 12 + -0.5m + m2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -0.5m + m2 = 0 + 12
-0.5m + m2 = 0 + 12

Combine like terms: 0 + 12 = 12
-0.5m + m2 = 12

The m term is -0.5m.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5m + 0.0625 + m2 = 12 + 0.0625

Reorder the terms:
0.0625 + -0.5m + m2 = 12 + 0.0625

Combine like terms: 12 + 0.0625 = 12.0625
0.0625 + -0.5m + m2 = 12.0625

Factor a perfect square on the left side:
(m + -0.25)(m + -0.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(m + -0.25) equal to 3.473110997 and -3.473110997.


Subproblem 1
m + -0.25 = 3.473110997

Simplifying
m + -0.25 = 3.473110997

Reorder the terms:
-0.25 + m = 3.473110997

Solving
-0.25 + m = 3.473110997

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = 3.473110997 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = 3.473110997 + 0.25
m = 3.473110997 + 0.25

Combine like terms: 3.473110997 + 0.25 = 3.723110997
m = 3.723110997

Simplifying
m = 3.723110997


Subproblem 2
m + -0.25 = -3.473110997

Simplifying
m + -0.25 = -3.473110997

Reorder the terms:
-0.25 + m = -3.473110997

Solving
-0.25 + m = -3.473110997

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = -3.473110997 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = -3.473110997 + 0.25
m = -3.473110997 + 0.25

Combine like terms: -3.473110997 + 0.25 = -3.223110997
m = -3.223110997

Simplifying
m = -3.223110997


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.723110997, -3.223110997}
Solution
m = {3.723110997, -3.223110997}

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