m^2-12m+33=0

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Solution for m^2-12m+33=0 equation:


Simplifying
m2 + -12m + 33 = 0

Reorder the terms:
33 + -12m + m2 = 0

Solving
33 + -12m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -12m + -33 + m2 = 0 + -33

Reorder the terms:
33 + -33 + -12m + m2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -12m + m2 = 0 + -33
-12m + m2 = 0 + -33

Combine like terms: 0 + -33 = -33
-12m + m2 = -33

The m term is -12m.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12m + 36 + m2 = -33 + 36

Reorder the terms:
36 + -12m + m2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + -12m + m2 = 3

Factor a perfect square on the left side:
(m + -6)(m + -6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(m + -6) equal to 1.732050808 and -1.732050808.

Subproblem 1

m + -6 = 1.732050808 Simplifying m + -6 = 1.732050808 Reorder the terms: -6 + m = 1.732050808 Solving -6 + m = 1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = 1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + m = 1.732050808 + 6 m = 1.732050808 + 6 Combine like terms: 1.732050808 + 6 = 7.732050808 m = 7.732050808 Simplifying m = 7.732050808

Subproblem 2

m + -6 = -1.732050808 Simplifying m + -6 = -1.732050808 Reorder the terms: -6 + m = -1.732050808 Solving -6 + m = -1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = -1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + m = -1.732050808 + 6 m = -1.732050808 + 6 Combine like terms: -1.732050808 + 6 = 4.267949192 m = 4.267949192 Simplifying m = 4.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. m = {7.732050808, 4.267949192}

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