7m^2-35m=-6+8

Solution for 7m^2-35m=-6+8 equation:

Simplifying
7m2 + -35m = -6 + 8

Reorder the terms:
-35m + 7m2 = -6 + 8

Combine like terms: -6 + 8 = 2
-35m + 7m2 = 2

Solving
-35m + 7m2 = 2

Solving for variable 'm'.

Reorder the terms:
-2 + -35m + 7m2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -35m + 7m2 = 0

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

Divide each side by '7'.
-0.2857142857 + -5m + m2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -5m + 0.2857142857 + m2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -5m + m2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -5m + m2 = 0 + 0.2857142857
-5m + m2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-5m + m2 = 0.2857142857

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 = 0.2857142857 + 6.25

Reorder the terms:
6.25 + -5m + m2 = 0.2857142857 + 6.25

Combine like terms: 0.2857142857 + 6.25 = 6.5357142857
6.25 + -5m + m2 = 6.5357142857

Factor a perfect square on the left side:
(m + -2.5)(m + -2.5) = 6.5357142857

Calculate the square root of the right side: 2.55650431

Break this problem into two subproblems by setting 
(m + -2.5) equal to 2.55650431 and -2.55650431.

Subproblem 1
m + -2.5 = 2.55650431

Simplifying
m + -2.5 = 2.55650431

Reorder the terms:
-2.5 + m = 2.55650431

Solving
-2.5 + m = 2.55650431

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 = 2.55650431 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = 2.55650431 + 2.5
m = 2.55650431 + 2.5

Combine like terms: 2.55650431 + 2.5 = 5.05650431
m = 5.05650431

Simplifying
m = 5.05650431

Subproblem 2
m + -2.5 = -2.55650431

Simplifying
m + -2.5 = -2.55650431

Reorder the terms:
-2.5 + m = -2.55650431

Solving
-2.5 + m = -2.55650431

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 = -2.55650431 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = -2.55650431 + 2.5
m = -2.55650431 + 2.5

Combine like terms: -2.55650431 + 2.5 = -0.05650431
m = -0.05650431

Simplifying
m = -0.05650431

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.05650431, -0.05650431}