7m^2+8m-2=0

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Solution for 7m^2+8m-2=0 equation:


Simplifying
7m2 + 8m + -2 = 0

Reorder the terms:
-2 + 8m + 7m2 = 0

Solving
-2 + 8m + 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 + 1.142857143m + m2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 1.142857143m + 0.2857142857 + m2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 1.142857143m + m2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 1.142857143m + m2 = 0 + 0.2857142857
1.142857143m + m2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
1.142857143m + m2 = 0.2857142857

The m term is 1.142857143m.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143m + 0.3265306123 + m2 = 0.2857142857 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143m + m2 = 0.2857142857 + 0.3265306123

Combine like terms: 0.2857142857 + 0.3265306123 = 0.612244898
0.3265306123 + 1.142857143m + m2 = 0.612244898

Factor a perfect square on the left side:
(m + 0.5714285715)(m + 0.5714285715) = 0.612244898

Calculate the square root of the right side: 0.782460796

Break this problem into two subproblems by setting 
(m + 0.5714285715) equal to 0.782460796 and -0.782460796.

Subproblem 1

m + 0.5714285715 = 0.782460796 Simplifying m + 0.5714285715 = 0.782460796 Reorder the terms: 0.5714285715 + m = 0.782460796 Solving 0.5714285715 + m = 0.782460796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + m = 0.782460796 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = 0.782460796 + -0.5714285715 m = 0.782460796 + -0.5714285715 Combine like terms: 0.782460796 + -0.5714285715 = 0.2110322245 m = 0.2110322245 Simplifying m = 0.2110322245

Subproblem 2

m + 0.5714285715 = -0.782460796 Simplifying m + 0.5714285715 = -0.782460796 Reorder the terms: 0.5714285715 + m = -0.782460796 Solving 0.5714285715 + m = -0.782460796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + m = -0.782460796 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = -0.782460796 + -0.5714285715 m = -0.782460796 + -0.5714285715 Combine like terms: -0.782460796 + -0.5714285715 = -1.3538893675 m = -1.3538893675 Simplifying m = -1.3538893675

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.2110322245, -1.3538893675}

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