m^2-11m+12=0

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Solution for m^2-11m+12=0 equation:


Simplifying
m2 + -11m + 12 = 0

Reorder the terms:
12 + -11m + m2 = 0

Solving
12 + -11m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -11m + -12 + m2 = 0 + -12

Reorder the terms:
12 + -12 + -11m + m2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -11m + m2 = 0 + -12
-11m + m2 = 0 + -12

Combine like terms: 0 + -12 = -12
-11m + m2 = -12

The m term is -11m.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11m + 30.25 + m2 = -12 + 30.25

Reorder the terms:
30.25 + -11m + m2 = -12 + 30.25

Combine like terms: -12 + 30.25 = 18.25
30.25 + -11m + m2 = 18.25

Factor a perfect square on the left side:
(m + -5.5)(m + -5.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(m + -5.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

m + -5.5 = 4.272001873 Simplifying m + -5.5 = 4.272001873 Reorder the terms: -5.5 + m = 4.272001873 Solving -5.5 + m = 4.272001873 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = 4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 4.272001873 + 5.5 m = 4.272001873 + 5.5 Combine like terms: 4.272001873 + 5.5 = 9.772001873 m = 9.772001873 Simplifying m = 9.772001873

Subproblem 2

m + -5.5 = -4.272001873 Simplifying m + -5.5 = -4.272001873 Reorder the terms: -5.5 + m = -4.272001873 Solving -5.5 + m = -4.272001873 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = -4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -4.272001873 + 5.5 m = -4.272001873 + 5.5 Combine like terms: -4.272001873 + 5.5 = 1.227998127 m = 1.227998127 Simplifying m = 1.227998127

Solution

The solution to the problem is based on the solutions from the subproblems. m = {9.772001873, 1.227998127}

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