-2m^2+18m-33=0

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Solution for -2m^2+18m-33=0 equation:


Simplifying
-2m2 + 18m + -33 = 0

Reorder the terms:
-33 + 18m + -2m2 = 0

Solving
-33 + 18m + -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'.
16.5 + -9m + m2 = 0

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + -9m + -16.5 + m2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + -9m + m2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + -9m + m2 = 0 + -16.5
-9m + m2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
-9m + m2 = -16.5

The m term is -9m.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9m + 20.25 + m2 = -16.5 + 20.25

Reorder the terms:
20.25 + -9m + m2 = -16.5 + 20.25

Combine like terms: -16.5 + 20.25 = 3.75
20.25 + -9m + m2 = 3.75

Factor a perfect square on the left side:
(m + -4.5)(m + -4.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(m + -4.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

m + -4.5 = 1.936491673 Simplifying m + -4.5 = 1.936491673 Reorder the terms: -4.5 + m = 1.936491673 Solving -4.5 + m = 1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = 1.936491673 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = 1.936491673 + 4.5 m = 1.936491673 + 4.5 Combine like terms: 1.936491673 + 4.5 = 6.436491673 m = 6.436491673 Simplifying m = 6.436491673

Subproblem 2

m + -4.5 = -1.936491673 Simplifying m + -4.5 = -1.936491673 Reorder the terms: -4.5 + m = -1.936491673 Solving -4.5 + m = -1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = -1.936491673 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = -1.936491673 + 4.5 m = -1.936491673 + 4.5 Combine like terms: -1.936491673 + 4.5 = 2.563508327 m = 2.563508327 Simplifying m = 2.563508327

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.436491673, 2.563508327}

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