7m^2-4m-2=0

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Solution for 7m^2-4m-2=0 equation: 


Simplifying
7m2 + -4m + -2 = 0

Reorder the terms:
-2 + -4m + 7m2 = 0

Solving
-2 + -4m + 7m2 = 0

Solving for variable 'm'.

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

Divide each side by '7'.
-0.2857142857 + -0.5714285714m + m2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.5714285714m + 0.2857142857 + m2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.5714285714m + m2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.5714285714m + m2 = 0 + 0.2857142857
-0.5714285714m + m2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.5714285714m + m2 = 0.2857142857

The m term is -0.5714285714m.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714m + 0.08163265305 + m2 = 0.2857142857 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714m + m2 = 0.2857142857 + 0.08163265305

Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875
0.08163265305 + -0.5714285714m + m2 = 0.36734693875

Factor a perfect square on the left side:
(m + -0.2857142857)(m + -0.2857142857) = 0.36734693875

Calculate the square root of the right side: 0.606091527

Break this problem into two subproblems by setting 
(m + -0.2857142857) equal to 0.606091527 and -0.606091527.


Subproblem 1
m + -0.2857142857 = 0.606091527

Simplifying
m + -0.2857142857 = 0.606091527

Reorder the terms:
-0.2857142857 + m = 0.606091527

Solving
-0.2857142857 + m = 0.606091527

Solving for variable 'm'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + m = 0.606091527 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + m = 0.606091527 + 0.2857142857
m = 0.606091527 + 0.2857142857

Combine like terms: 0.606091527 + 0.2857142857 = 0.8918058127
m = 0.8918058127

Simplifying
m = 0.8918058127


Subproblem 2
m + -0.2857142857 = -0.606091527

Simplifying
m + -0.2857142857 = -0.606091527

Reorder the terms:
-0.2857142857 + m = -0.606091527

Solving
-0.2857142857 + m = -0.606091527

Solving for variable 'm'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + m = -0.606091527 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + m = -0.606091527 + 0.2857142857
m = -0.606091527 + 0.2857142857

Combine like terms: -0.606091527 + 0.2857142857 = -0.3203772413
m = -0.3203772413

Simplifying
m = -0.3203772413


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.8918058127, -0.3203772413}

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