-2m^2+6m+27=

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Solution for -2m^2+6m+27= equation:


Simplifying
-2m2 + 6m + 27 = 0

Reorder the terms:
27 + 6m + -2m2 = 0

Solving
27 + 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'.
-13.5 + -3m + m2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -3m + 13.5 + m2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -3m + m2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -3m + m2 = 0 + 13.5
-3m + m2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-3m + m2 = 13.5

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 = 13.5 + 2.25

Reorder the terms:
2.25 + -3m + m2 = 13.5 + 2.25

Combine like terms: 13.5 + 2.25 = 15.75
2.25 + -3m + m2 = 15.75

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(m + -1.5) equal to 3.968626967 and -3.968626967.

Subproblem 1

m + -1.5 = 3.968626967 Simplifying m + -1.5 = 3.968626967 Reorder the terms: -1.5 + m = 3.968626967 Solving -1.5 + m = 3.968626967 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 = 3.968626967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 3.968626967 + 1.5 m = 3.968626967 + 1.5 Combine like terms: 3.968626967 + 1.5 = 5.468626967 m = 5.468626967 Simplifying m = 5.468626967

Subproblem 2

m + -1.5 = -3.968626967 Simplifying m + -1.5 = -3.968626967 Reorder the terms: -1.5 + m = -3.968626967 Solving -1.5 + m = -3.968626967 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 = -3.968626967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -3.968626967 + 1.5 m = -3.968626967 + 1.5 Combine like terms: -3.968626967 + 1.5 = -2.468626967 m = -2.468626967 Simplifying m = -2.468626967

Solution

The solution to the problem is based on the solutions from the subproblems. m = {5.468626967, -2.468626967}

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