5m^2-2m=8

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Solution for 5m^2-2m=8 equation:


Simplifying
5m2 + -2m = 8

Reorder the terms:
-2m + 5m2 = 8

Solving
-2m + 5m2 = 8

Solving for variable 'm'.

Reorder the terms:
-8 + -2m + 5m2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -2m + 5m2 = 0

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

Divide each side by '5'.
-1.6 + -0.4m + m2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.4m + 1.6 + m2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.4m + m2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.4m + m2 = 0 + 1.6
-0.4m + m2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.4m + m2 = 1.6

The m term is -0.4m.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4m + 0.04 + m2 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4m + m2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4m + m2 = 1.64

Factor a perfect square on the left side:
(m + -0.2)(m + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(m + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1

m + -0.2 = 1.280624847 Simplifying m + -0.2 = 1.280624847 Reorder the terms: -0.2 + m = 1.280624847 Solving -0.2 + m = 1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 1.280624847 + 0.2 m = 1.280624847 + 0.2 Combine like terms: 1.280624847 + 0.2 = 1.480624847 m = 1.480624847 Simplifying m = 1.480624847

Subproblem 2

m + -0.2 = -1.280624847 Simplifying m + -0.2 = -1.280624847 Reorder the terms: -0.2 + m = -1.280624847 Solving -0.2 + m = -1.280624847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -1.280624847 + 0.2 m = -1.280624847 + 0.2 Combine like terms: -1.280624847 + 0.2 = -1.080624847 m = -1.080624847 Simplifying m = -1.080624847

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.480624847, -1.080624847}

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