3m^2+10m-9=0

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Solution for 3m^2+10m-9=0 equation:


Simplifying
3m2 + 10m + -9 = 0

Reorder the terms:
-9 + 10m + 3m2 = 0

Solving
-9 + 10m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
-3 + 3.333333333m + m2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.333333333m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.333333333m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.333333333m + m2 = 0 + 3
3.333333333m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.333333333m + m2 = 3

The m term is 3.333333333m.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333m + 2.777777779 + m2 = 3 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333m + m2 = 3 + 2.777777779

Combine like terms: 3 + 2.777777779 = 5.777777779
2.777777779 + 3.333333333m + m2 = 5.777777779

Factor a perfect square on the left side:
(m + 1.666666667)(m + 1.666666667) = 5.777777779

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(m + 1.666666667) equal to 2.403700851 and -2.403700851.

Subproblem 1

m + 1.666666667 = 2.403700851 Simplifying m + 1.666666667 = 2.403700851 Reorder the terms: 1.666666667 + m = 2.403700851 Solving 1.666666667 + m = 2.403700851 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + m = 2.403700851 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + m = 2.403700851 + -1.666666667 m = 2.403700851 + -1.666666667 Combine like terms: 2.403700851 + -1.666666667 = 0.737034184 m = 0.737034184 Simplifying m = 0.737034184

Subproblem 2

m + 1.666666667 = -2.403700851 Simplifying m + 1.666666667 = -2.403700851 Reorder the terms: 1.666666667 + m = -2.403700851 Solving 1.666666667 + m = -2.403700851 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + m = -2.403700851 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + m = -2.403700851 + -1.666666667 m = -2.403700851 + -1.666666667 Combine like terms: -2.403700851 + -1.666666667 = -4.070367518 m = -4.070367518 Simplifying m = -4.070367518

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.737034184, -4.070367518}

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