2m^2+18m+33=7

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Solution for 2m^2+18m+33=7 equation: 


Simplifying
2m2 + 18m + 33 = 7

Reorder the terms:
33 + 18m + 2m2 = 7

Solving
33 + 18m + 2m2 = 7

Solving for variable 'm'.

Reorder the terms:
33 + -7 + 18m + 2m2 = 7 + -7

Combine like terms: 33 + -7 = 26
26 + 18m + 2m2 = 7 + -7

Combine like terms: 7 + -7 = 0
26 + 18m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 9m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 9m + m2)' equal to zero and attempt to solve:

Simplifying
13 + 9m + m2 = 0

Solving
13 + 9m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 9m + -13 + m2 = 0 + -13

Reorder the terms:
13 + -13 + 9m + m2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 9m + m2 = 0 + -13
9m + m2 = 0 + -13

Combine like terms: 0 + -13 = -13
9m + m2 = -13

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 = -13 + 20.25

Reorder the terms:
20.25 + 9m + m2 = -13 + 20.25

Combine like terms: -13 + 20.25 = 7.25
20.25 + 9m + m2 = 7.25

Factor a perfect square on the left side:
(m + 4.5)(m + 4.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(m + 4.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
m + 4.5 = 2.692582404

Simplifying
m + 4.5 = 2.692582404

Reorder the terms:
4.5 + m = 2.692582404

Solving
4.5 + m = 2.692582404

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 = 2.692582404 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + m = 2.692582404 + -4.5
m = 2.692582404 + -4.5

Combine like terms: 2.692582404 + -4.5 = -1.807417596
m = -1.807417596

Simplifying
m = -1.807417596


Subproblem 2
m + 4.5 = -2.692582404

Simplifying
m + 4.5 = -2.692582404

Reorder the terms:
4.5 + m = -2.692582404

Solving
4.5 + m = -2.692582404

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 = -2.692582404 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + m = -2.692582404 + -4.5
m = -2.692582404 + -4.5

Combine like terms: -2.692582404 + -4.5 = -7.192582404
m = -7.192582404

Simplifying
m = -7.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.807417596, -7.192582404}
Solution
m = {-1.807417596, -7.192582404}

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