4m^2-38m-3=0

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Solution for 4m^2-38m-3=0 equation: 


Simplifying
4m2 + -38m + -3 = 0

Reorder the terms:
-3 + -38m + 4m2 = 0

Solving
-3 + -38m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
-0.75 + -9.5m + m2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -9.5m + 0.75 + m2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -9.5m + m2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -9.5m + m2 = 0 + 0.75
-9.5m + m2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-9.5m + m2 = 0.75

The m term is -9.5m.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5m + 22.5625 + m2 = 0.75 + 22.5625

Reorder the terms:
22.5625 + -9.5m + m2 = 0.75 + 22.5625

Combine like terms: 0.75 + 22.5625 = 23.3125
22.5625 + -9.5m + m2 = 23.3125

Factor a perfect square on the left side:
(m + -4.75)(m + -4.75) = 23.3125

Calculate the square root of the right side: 4.828301979

Break this problem into two subproblems by setting 
(m + -4.75) equal to 4.828301979 and -4.828301979.


Subproblem 1
m + -4.75 = 4.828301979

Simplifying
m + -4.75 = 4.828301979

Reorder the terms:
-4.75 + m = 4.828301979

Solving
-4.75 + m = 4.828301979

Solving for variable 'm'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + m = 4.828301979 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + m = 4.828301979 + 4.75
m = 4.828301979 + 4.75

Combine like terms: 4.828301979 + 4.75 = 9.578301979
m = 9.578301979

Simplifying
m = 9.578301979


Subproblem 2
m + -4.75 = -4.828301979

Simplifying
m + -4.75 = -4.828301979

Reorder the terms:
-4.75 + m = -4.828301979

Solving
-4.75 + m = -4.828301979

Solving for variable 'm'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + m = -4.828301979 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + m = -4.828301979 + 4.75
m = -4.828301979 + 4.75

Combine like terms: -4.828301979 + 4.75 = -0.078301979
m = -0.078301979

Simplifying
m = -0.078301979


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.578301979, -0.078301979}

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