m^2+m+1=19

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Solution for m^2+m+1=19 equation:


Simplifying
m2 + m + 1 = 19

Reorder the terms:
1 + m + m2 = 19

Solving
1 + m + m2 = 19

Solving for variable 'm'.

Reorder the terms:
1 + -19 + m + m2 = 19 + -19

Combine like terms: 1 + -19 = -18
-18 + m + m2 = 19 + -19

Combine like terms: 19 + -19 = 0
-18 + m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + m + 18 + m2 = 0 + 18

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

Combine like terms: -18 + 18 = 0
0 + m + m2 = 0 + 18
m + m2 = 0 + 18

Combine like terms: 0 + 18 = 18
m + m2 = 18

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
m + 0.25 + m2 = 18 + 0.25

Reorder the terms:
0.25 + m + m2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + m + m2 = 18.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(m + 0.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
m + 0.5 = 4.272001873

Simplifying
m + 0.5 = 4.272001873

Reorder the terms:
0.5 + m = 4.272001873

Solving
0.5 + m = 4.272001873

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 4.272001873 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 4.272001873 + -0.5
m = 4.272001873 + -0.5

Combine like terms: 4.272001873 + -0.5 = 3.772001873
m = 3.772001873

Simplifying
m = 3.772001873


Subproblem 2
m + 0.5 = -4.272001873

Simplifying
m + 0.5 = -4.272001873

Reorder the terms:
0.5 + m = -4.272001873

Solving
0.5 + m = -4.272001873

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -4.272001873 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -4.272001873 + -0.5
m = -4.272001873 + -0.5

Combine like terms: -4.272001873 + -0.5 = -4.772001873
m = -4.772001873

Simplifying
m = -4.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.772001873, -4.772001873}

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