0=-3m^2+6m+1

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Solution for 0=-3m^2+6m+1 equation:


Simplifying
0 = -3m2 + 6m + 1

Reorder the terms:
0 = 1 + 6m + -3m2

Solving
0 = 1 + 6m + -3m2

Solving for variable 'm'.

Combine like terms: 0 + -1 = -1
-1 + -6m + 3m2 = 1 + 6m + -3m2 + -1 + -6m + 3m2

Reorder the terms:
-1 + -6m + 3m2 = 1 + -1 + 6m + -6m + -3m2 + 3m2

Combine like terms: 1 + -1 = 0
-1 + -6m + 3m2 = 0 + 6m + -6m + -3m2 + 3m2
-1 + -6m + 3m2 = 6m + -6m + -3m2 + 3m2

Combine like terms: 6m + -6m = 0
-1 + -6m + 3m2 = 0 + -3m2 + 3m2
-1 + -6m + 3m2 = -3m2 + 3m2

Combine like terms: -3m2 + 3m2 = 0
-1 + -6m + 3m2 = 0

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

Divide each side by '3'.
-0.3333333333 + -2m + m2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2m + 0.3333333333 + m2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2m + m2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2m + m2 = 0 + 0.3333333333
-2m + m2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2m + m2 = 0.3333333333

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 = 0.3333333333 + 1

Reorder the terms:
1 + -2m + m2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + -2m + m2 = 1.3333333333

Factor a perfect square on the left side:
(m + -1)(m + -1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(m + -1) equal to 1.154700538 and -1.154700538.

Subproblem 1

m + -1 = 1.154700538 Simplifying m + -1 = 1.154700538 Reorder the terms: -1 + m = 1.154700538 Solving -1 + m = 1.154700538 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 = 1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.154700538 + 1 m = 1.154700538 + 1 Combine like terms: 1.154700538 + 1 = 2.154700538 m = 2.154700538 Simplifying m = 2.154700538

Subproblem 2

m + -1 = -1.154700538 Simplifying m + -1 = -1.154700538 Reorder the terms: -1 + m = -1.154700538 Solving -1 + m = -1.154700538 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 = -1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.154700538 + 1 m = -1.154700538 + 1 Combine like terms: -1.154700538 + 1 = -0.154700538 m = -0.154700538 Simplifying m = -0.154700538

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.154700538, -0.154700538}

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