4m^2+8m-73=0

Solution for 4m^2+8m-73=0 equation:

Simplifying
4m2 + 8m + -73 = 0

Reorder the terms:
-73 + 8m + 4m2 = 0

Solving
-73 + 8m + 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'.
-18.25 + 2m + m2 = 0

Move the constant term to the right:

Add '18.25' to each side of the equation.
-18.25 + 2m + 18.25 + m2 = 0 + 18.25

Reorder the terms:
-18.25 + 18.25 + 2m + m2 = 0 + 18.25

Combine like terms: -18.25 + 18.25 = 0.00
0.00 + 2m + m2 = 0 + 18.25
2m + m2 = 0 + 18.25

Combine like terms: 0 + 18.25 = 18.25
2m + m2 = 18.25

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 = 18.25 + 1

Reorder the terms:
1 + 2m + m2 = 18.25 + 1

Combine like terms: 18.25 + 1 = 19.25
1 + 2m + m2 = 19.25

Factor a perfect square on the left side:
(m + 1)(m + 1) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(m + 1) equal to 4.387482194 and -4.387482194.

Subproblem 1
m + 1 = 4.387482194

Simplifying
m + 1 = 4.387482194

Reorder the terms:
1 + m = 4.387482194

Solving
1 + m = 4.387482194

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 = 4.387482194 + -1

Combine like terms: 1 + -1 = 0
0 + m = 4.387482194 + -1
m = 4.387482194 + -1

Combine like terms: 4.387482194 + -1 = 3.387482194
m = 3.387482194

Simplifying
m = 3.387482194

Subproblem 2
m + 1 = -4.387482194

Simplifying
m + 1 = -4.387482194

Reorder the terms:
1 + m = -4.387482194

Solving
1 + m = -4.387482194

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 = -4.387482194 + -1

Combine like terms: 1 + -1 = 0
0 + m = -4.387482194 + -1
m = -4.387482194 + -1

Combine like terms: -4.387482194 + -1 = -5.387482194
m = -5.387482194

Simplifying
m = -5.387482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.387482194, -5.387482194}