2m^2-6m-15=0

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Solution for 2m^2-6m-15=0 equation:


Simplifying
2m2 + -6m + -15 = 0

Reorder the terms:
-15 + -6m + 2m2 = 0

Solving
-15 + -6m + 2m2 = 0

Solving for variable 'm'.

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

Divide each side by '2'.
-7.5 + -3m + m2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3m + 7.5 + m2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3m + m2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3m + m2 = 0 + 7.5
-3m + m2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-3m + m2 = 7.5

The m term is -3m.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3m + 2.25 + m2 = 7.5 + 2.25

Reorder the terms:
2.25 + -3m + m2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + -3m + m2 = 9.75

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(m + -1.5) equal to 3.122498999 and -3.122498999.

Subproblem 1

m + -1.5 = 3.122498999 Simplifying m + -1.5 = 3.122498999 Reorder the terms: -1.5 + m = 3.122498999 Solving -1.5 + m = 3.122498999 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = 3.122498999 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 3.122498999 + 1.5 m = 3.122498999 + 1.5 Combine like terms: 3.122498999 + 1.5 = 4.622498999 m = 4.622498999 Simplifying m = 4.622498999

Subproblem 2

m + -1.5 = -3.122498999 Simplifying m + -1.5 = -3.122498999 Reorder the terms: -1.5 + m = -3.122498999 Solving -1.5 + m = -3.122498999 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = -3.122498999 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -3.122498999 + 1.5 m = -3.122498999 + 1.5 Combine like terms: -3.122498999 + 1.5 = -1.622498999 m = -1.622498999 Simplifying m = -1.622498999

Solution

The solution to the problem is based on the solutions from the subproblems. m = {4.622498999, -1.622498999}

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