5m^2-40m+5=0

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


Simplifying
5m2 + -40m + 5 = 0

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

Solving
5 + -40m + 5m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -8m + m2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -8m + m2)' equal to zero and attempt to solve:

Simplifying
1 + -8m + m2 = 0

Solving
1 + -8m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -8m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + -8m + m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8m + m2 = 0 + -1
-8m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8m + m2 = -1

The m term is -8m.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8m + 16 + m2 = -1 + 16

Reorder the terms:
16 + -8m + m2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + -8m + m2 = 15

Factor a perfect square on the left side:
(m + -4)(m + -4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(m + -4) equal to 3.872983346 and -3.872983346.


Subproblem 1
m + -4 = 3.872983346

Simplifying
m + -4 = 3.872983346

Reorder the terms:
-4 + m = 3.872983346

Solving
-4 + m = 3.872983346

Solving for variable 'm'.

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

Add '4' to each side of the equation.
-4 + 4 + m = 3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + m = 3.872983346 + 4
m = 3.872983346 + 4

Combine like terms: 3.872983346 + 4 = 7.872983346
m = 7.872983346

Simplifying
m = 7.872983346


Subproblem 2
m + -4 = -3.872983346

Simplifying
m + -4 = -3.872983346

Reorder the terms:
-4 + m = -3.872983346

Solving
-4 + m = -3.872983346

Solving for variable 'm'.

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

Add '4' to each side of the equation.
-4 + 4 + m = -3.872983346 + 4

Combine like terms: -4 + 4 = 0
0 + m = -3.872983346 + 4
m = -3.872983346 + 4

Combine like terms: -3.872983346 + 4 = 0.127016654
m = 0.127016654

Simplifying
m = 0.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.872983346, 0.127016654}
Solution
m = {7.872983346, 0.127016654}

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