12m^2-24m+5=

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Solution for 12m^2-24m+5= equation:


Simplifying
12m2 + -24m + 5 = 0

Reorder the terms:
5 + -24m + 12m2 = 0

Solving
5 + -24m + 12m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.4166666667 + -2m + m2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -2m + -0.4166666667 + m2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + -2m + m2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + -2m + m2 = 0 + -0.4166666667
-2m + m2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
-2m + m2 = -0.4166666667

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = -0.4166666667 + 1

Reorder the terms:
1 + -2m + m2 = -0.4166666667 + 1

Combine like terms: -0.4166666667 + 1 = 0.5833333333
1 + -2m + m2 = 0.5833333333

Factor a perfect square on the left side:
(m + -1)(m + -1) = 0.5833333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(m + -1) equal to 0.763762616 and -0.763762616.

Subproblem 1

m + -1 = 0.763762616 Simplifying m + -1 = 0.763762616 Reorder the terms: -1 + m = 0.763762616 Solving -1 + m = 0.763762616 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 0.763762616 + 1 Combine like terms: -1 + 1 = 0 0 + m = 0.763762616 + 1 m = 0.763762616 + 1 Combine like terms: 0.763762616 + 1 = 1.763762616 m = 1.763762616 Simplifying m = 1.763762616

Subproblem 2

m + -1 = -0.763762616 Simplifying m + -1 = -0.763762616 Reorder the terms: -1 + m = -0.763762616 Solving -1 + m = -0.763762616 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -0.763762616 + 1 Combine like terms: -1 + 1 = 0 0 + m = -0.763762616 + 1 m = -0.763762616 + 1 Combine like terms: -0.763762616 + 1 = 0.236237384 m = 0.236237384 Simplifying m = 0.236237384

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.763762616, 0.236237384}

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