5m^2+18m-16=0

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Solution for 5m^2+18m-16=0 equation:


Simplifying
5m2 + 18m + -16 = 0

Reorder the terms:
-16 + 18m + 5m2 = 0

Solving
-16 + 18m + 5m2 = 0

Solving for variable 'm'.

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

Divide each side by '5'.
-3.2 + 3.6m + m2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 3.6m + 3.2 + m2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 3.6m + m2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 3.6m + m2 = 0 + 3.2
3.6m + m2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
3.6m + m2 = 3.2

The m term is 3.6m.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6m + 3.24 + m2 = 3.2 + 3.24

Reorder the terms:
3.24 + 3.6m + m2 = 3.2 + 3.24

Combine like terms: 3.2 + 3.24 = 6.44
3.24 + 3.6m + m2 = 6.44

Factor a perfect square on the left side:
(m + 1.8)(m + 1.8) = 6.44

Calculate the square root of the right side: 2.537715508

Break this problem into two subproblems by setting 
(m + 1.8) equal to 2.537715508 and -2.537715508.

Subproblem 1

m + 1.8 = 2.537715508 Simplifying m + 1.8 = 2.537715508 Reorder the terms: 1.8 + m = 2.537715508 Solving 1.8 + m = 2.537715508 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + m = 2.537715508 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + m = 2.537715508 + -1.8 m = 2.537715508 + -1.8 Combine like terms: 2.537715508 + -1.8 = 0.737715508 m = 0.737715508 Simplifying m = 0.737715508

Subproblem 2

m + 1.8 = -2.537715508 Simplifying m + 1.8 = -2.537715508 Reorder the terms: 1.8 + m = -2.537715508 Solving 1.8 + m = -2.537715508 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + m = -2.537715508 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + m = -2.537715508 + -1.8 m = -2.537715508 + -1.8 Combine like terms: -2.537715508 + -1.8 = -4.337715508 m = -4.337715508 Simplifying m = -4.337715508

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.737715508, -4.337715508}

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