7m^2=8m-2

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


Simplifying
7m2 = 8m + -2

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

Solving
7m2 = -2 + 8m

Solving for variable 'm'.

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

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

Combine like terms: -2 + 2 = 0
2 + -8m + 7m2 = 0 + 8m + -8m
2 + -8m + 7m2 = 8m + -8m

Combine like terms: 8m + -8m = 0
2 + -8m + 7m2 = 0

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 = 0.0408163266
0.3265306123 + -1.142857143m + m2 = 0.0408163266

Factor a perfect square on the left side:
(m + -0.5714285715)(m + -0.5714285715) = 0.0408163266

Calculate the square root of the right side: 0.202030509

Break this problem into two subproblems by setting 
(m + -0.5714285715) equal to 0.202030509 and -0.202030509.

Subproblem 1

m + -0.5714285715 = 0.202030509 Simplifying m + -0.5714285715 = 0.202030509 Reorder the terms: -0.5714285715 + m = 0.202030509 Solving -0.5714285715 + m = 0.202030509 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 = 0.202030509 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + m = 0.202030509 + 0.5714285715 m = 0.202030509 + 0.5714285715 Combine like terms: 0.202030509 + 0.5714285715 = 0.7734590805 m = 0.7734590805 Simplifying m = 0.7734590805

Subproblem 2

m + -0.5714285715 = -0.202030509 Simplifying m + -0.5714285715 = -0.202030509 Reorder the terms: -0.5714285715 + m = -0.202030509 Solving -0.5714285715 + m = -0.202030509 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 = -0.202030509 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + m = -0.202030509 + 0.5714285715 m = -0.202030509 + 0.5714285715 Combine like terms: -0.202030509 + 0.5714285715 = 0.3693980625 m = 0.3693980625 Simplifying m = 0.3693980625

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.7734590805, 0.3693980625}

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