m^2+5m-40=0

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Solution for m^2+5m-40=0 equation: 


Simplifying
m2 + 5m + -40 = 0

Reorder the terms:
-40 + 5m + m2 = 0

Solving
-40 + 5m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 5m + 40 + m2 = 0 + 40

Reorder the terms:
-40 + 40 + 5m + m2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 5m + m2 = 0 + 40
5m + m2 = 0 + 40

Combine like terms: 0 + 40 = 40
5m + m2 = 40

The m term is 5m.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m + 6.25 + m2 = 40 + 6.25

Reorder the terms:
6.25 + 5m + m2 = 40 + 6.25

Combine like terms: 40 + 6.25 = 46.25
6.25 + 5m + m2 = 46.25

Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(m + 2.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
m + 2.5 = 6.800735254

Simplifying
m + 2.5 = 6.800735254

Reorder the terms:
2.5 + m = 6.800735254

Solving
2.5 + m = 6.800735254

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = 6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = 6.800735254 + -2.5
m = 6.800735254 + -2.5

Combine like terms: 6.800735254 + -2.5 = 4.300735254
m = 4.300735254

Simplifying
m = 4.300735254


Subproblem 2
m + 2.5 = -6.800735254

Simplifying
m + 2.5 = -6.800735254

Reorder the terms:
2.5 + m = -6.800735254

Solving
2.5 + m = -6.800735254

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = -6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = -6.800735254 + -2.5
m = -6.800735254 + -2.5

Combine like terms: -6.800735254 + -2.5 = -9.300735254
m = -9.300735254

Simplifying
m = -9.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.300735254, -9.300735254}

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