9m^2-9m-2=0

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


Simplifying
9m2 + -9m + -2 = 0

Reorder the terms:
-2 + -9m + 9m2 = 0

Solving
-2 + -9m + 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'.
-0.2222222222 + -1m + m2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -1m + 0.2222222222 + m2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -1m + m2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -1m + m2 = 0 + 0.2222222222
-1m + m2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-1m + m2 = 0.2222222222

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 0.2222222222 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 0.2222222222 + 0.25

Combine like terms: 0.2222222222 + 0.25 = 0.4722222222
0.25 + -1m + m2 = 0.4722222222

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 0.4722222222

Calculate the square root of the right side: 0.687184271

Break this problem into two subproblems by setting 
(m + -0.5) equal to 0.687184271 and -0.687184271.

Subproblem 1

m + -0.5 = 0.687184271 Simplifying m + -0.5 = 0.687184271 Reorder the terms: -0.5 + m = 0.687184271 Solving -0.5 + m = 0.687184271 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = 0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 0.687184271 + 0.5 m = 0.687184271 + 0.5 Combine like terms: 0.687184271 + 0.5 = 1.187184271 m = 1.187184271 Simplifying m = 1.187184271

Subproblem 2

m + -0.5 = -0.687184271 Simplifying m + -0.5 = -0.687184271 Reorder the terms: -0.5 + m = -0.687184271 Solving -0.5 + m = -0.687184271 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = -0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -0.687184271 + 0.5 m = -0.687184271 + 0.5 Combine like terms: -0.687184271 + 0.5 = -0.187184271 m = -0.187184271 Simplifying m = -0.187184271

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.187184271, -0.187184271}

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