m^2+3m+1.5=0

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Solution for m^2+3m+1.5=0 equation: 


Simplifying
m2 + 3m + 1.5 = 0

Reorder the terms:
1.5 + 3m + m2 = 0

Solving
1.5 + 3m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3m + -1.5 + m2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 3m + m2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3m + m2 = 0 + -1.5
3m + m2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
3m + m2 = -1.5

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 = -1.5 + 2.25

Reorder the terms:
2.25 + 3m + m2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + 3m + m2 = 0.75

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(m + 1.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
m + 1.5 = 0.866025404

Simplifying
m + 1.5 = 0.866025404

Reorder the terms:
1.5 + m = 0.866025404

Solving
1.5 + m = 0.866025404

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 = 0.866025404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = 0.866025404 + -1.5
m = 0.866025404 + -1.5

Combine like terms: 0.866025404 + -1.5 = -0.633974596
m = -0.633974596

Simplifying
m = -0.633974596


Subproblem 2
m + 1.5 = -0.866025404

Simplifying
m + 1.5 = -0.866025404

Reorder the terms:
1.5 + m = -0.866025404

Solving
1.5 + m = -0.866025404

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 = -0.866025404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = -0.866025404 + -1.5
m = -0.866025404 + -1.5

Combine like terms: -0.866025404 + -1.5 = -2.366025404
m = -2.366025404

Simplifying
m = -2.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.633974596, -2.366025404}

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