9m^2-3m-5=0

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Solution for 9m^2-3m-5=0 equation: 


Simplifying
9m2 + -3m + -5 = 0

Reorder the terms:
-5 + -3m + 9m2 = 0

Solving
-5 + -3m + 9m2 = 0

Solving for variable 'm'.

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

Divide each side by '9'.
-0.5555555556 + -0.3333333333m + m2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + -0.3333333333m + 0.5555555556 + m2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + -0.3333333333m + m2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + -0.3333333333m + m2 = 0 + 0.5555555556
-0.3333333333m + m2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
-0.3333333333m + m2 = 0.5555555556

The m term is -0.3333333333m.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333m + 0.02777777779 + m2 = 0.5555555556 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333m + m2 = 0.5555555556 + 0.02777777779

Combine like terms: 0.5555555556 + 0.02777777779 = 0.58333333339
0.02777777779 + -0.3333333333m + m2 = 0.58333333339

Factor a perfect square on the left side:
(m + -0.1666666667)(m + -0.1666666667) = 0.58333333339

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(m + -0.1666666667) equal to 0.763762616 and -0.763762616.


Subproblem 1
m + -0.1666666667 = 0.763762616

Simplifying
m + -0.1666666667 = 0.763762616

Reorder the terms:
-0.1666666667 + m = 0.763762616

Solving
-0.1666666667 + m = 0.763762616

Solving for variable 'm'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + m = 0.763762616 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = 0.763762616 + 0.1666666667
m = 0.763762616 + 0.1666666667

Combine like terms: 0.763762616 + 0.1666666667 = 0.9304292827
m = 0.9304292827

Simplifying
m = 0.9304292827


Subproblem 2
m + -0.1666666667 = -0.763762616

Simplifying
m + -0.1666666667 = -0.763762616

Reorder the terms:
-0.1666666667 + m = -0.763762616

Solving
-0.1666666667 + m = -0.763762616

Solving for variable 'm'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + m = -0.763762616 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = -0.763762616 + 0.1666666667
m = -0.763762616 + 0.1666666667

Combine like terms: -0.763762616 + 0.1666666667 = -0.5970959493
m = -0.5970959493

Simplifying
m = -0.5970959493


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.9304292827, -0.5970959493}

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